Matrix-induced two-photon absorption in anthracene

Chemi~Physi~ 170 (1993) 185-192 Nosh-Ho~and

Matrix-induced two-photon absorption in anthracene

A. Bree and R. Zwarich Department of Cherntsty, University of&it&h Columbia, Vancouver, British Cohmbia, Canada V6T 121

Received 23 September 1992

The absorption spectrum and the two-photon excitation spectrum of anthracene in a carbazole matrix have been measured at 1.8 K in the wavelength range of the first absorption band near 400 nm. This transition is formally allowed as a one-photon but not as a two-photon process; however, two-photon mtensity is induced into the anthracene spectrum by the matrix. The intensity distribution along a Franck-Condon progression is not the same in the one- and two-photon spectra. Assuming that the vibroni- tally induced component of the two-photon spectrum is independent of the host, earlier intensity data taken in a fluorene host crystal can be scaled to the new data collected here. A simple model, set up in the deep trap limit, is used to account for these observed differences between the one- and two-photon spectra in the carbazole host and between fluorene and carbazole host materials.

1. Induction

There are a number of accounts of the two-photon excitation spectrum (TPES) [ l-71 of anthracene but only the most recent report [ 71 of the TPES of anthracene in fluorene and biphenyl host crystals at 4.2 K in the region of the lowest energy B,, state exam- ines the effect of the host matrix on this state. The transition in the anthracene guest molecule, ‘Blue’Ag, is one-photon allowed but two-photon forbidden. In the biphenyl host the origin band does not appear in the TPES, intensity being induced vibroni~lly with the involvement of some b,, vibrations of the excited state which appear to couple the B,, electronic state to an pLB. excited state near 29400 cm-i. In the fluorene host, on the other hand, the origin band together with some short progressions in a, modes appear, as well as the vibronically induced component. In the fluorene host lattice the molecular long axes L (we adopt a descriptive axis labelling L, M, N in which L is the long axis and N is the molecular normal) lies parallel to the c crystal axis [ 81, and this allows a clear experimental distinction to be made between the two-photon tensor elements fyLL and oMM. The c~stal-indu~d origin band was MM active while the vibronically induced part of the spectrum was LL active; in this way the two parts of the

TPES in fluorene were cleanly separated [ 7 ] . It was thought that the mat~x-induced component of the TPES appeared in MM because both the static dipole moment of the fluorene host molecules and the transition moment in anthracene lie parallel to M. In summary, the interpretation developed to account for the observed TPES in fluorene [ 7 ] was that the spectrum built on the origin arose through off-resonance coupling with states of fluorene while the vibration- ally induced spectrum is intramolecular within a pas- sive matrix.

One aim of the present paper was to provide more data to elucidate how the mat~x-induced intensity appears by recording the TPES of anthracene in a carbazole host crystal. Carbazole [ 9 ] has a crystal structure that is isomorphic with that of fluorene [ 81 but, for our own convenience, we have interchanged the b and c axes in the carbazole structure so that the space groups are the same (Pnam) for both crystals. The static dipole moment of fluorene has been found tobe0.28 [10],0.82 [11],0.53 [12] andOS8debye [ 131; the mean of these values is 0.55 debye. The dipole moment of carbazole is given as 2.09 [ 14 ] and 1.73 debye [ 151 from dielectric measurements, and either 1.9 or 1.6 debye from electro-optic absorption measurements [ 151. By measuring the intensity change in going from a fluorene matrix to carbazole,

0301-0104/93/s 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.

186 A. Bree and R. Zwarich /Chemical Physics 170 (1993) 185-l 92

we should see what role the static moment plays in inducing the MM component of the TPES.

Craig and Thirunamachandran [ 161 were the first to discuss the nature of excited electronic states of dilute mixed molecular crystals, outlining the effect the host lattice had on the excited states of the guest molecule. A later series of papers by Craig and Philpott [ 171 extended the theory to shallow and deep traps. A second aim of this work is to extend the deep trap model [ 16 ] to account for the TPES of anthracene in fluorene and carbazole hosts through the inclusion of the dipole moments of the host molecules.

2. Experimental

Carbazole (Eastman white label) was purified by recrystallization followed by zone-refining under vacuum. Anthracene was added to nominal mole fractions of 9 x lop4 and 2.9 x 10m5 and boules of the mixtures were grown using a Bridgman furnace. Sin- gle crystal portions of an ingot were selected by ex- amining the sample under a polarizing microscope; the appropriate crystal section was identified by con- oscopic examination and cut using a wire saw.

The excitation source was a Nd: YAG pumped dye laser from Quanta Ray which provided 10 ns pulses with energy in the range 1- 15 mJ. The dyes used were LDS 751 and LDS 698 from Exciton. A cylindrical lens with a 15 cm focal length was used to focus the light on to the sample when exciting into the first system of anthracene; this lens was not used when exciting into the host absorption system.

A portion of the incoming light pulse and the re- sponse from the sample were detected separately by photomultipliers, the resulting electrical signals being measured using gated integrators supplied by Stanford Research Systems. The gate width was set at 15 ns. The rest of the equipment used to record the spectra has been described in an earlier paper [ 18 1.

3. The model

We apply the theory presented by Craig and Thirunamachandran [ 161 for the deep trap limit which supposes that the host-host interactions are small compared with the host-guest energy separa-

tion. In this limit, the structure of the host bands is ignored. If the mixed crystal is sufficiently dilute, as here, guest-guest interactions may be neglected and we may assume there is only one guest in the crystal which occupies a site of type 1 in the mth unit cell. There are N host molecules and one guest in the crystal with h molecules in each cell. The crystal Hamil- tonian is then

H clystal=hlm+ c h,+ c ~lm,rr, rp# lm lP#lrn

+ cc v,,, 3 rPclq# Irn

(1)

where h, is the Hamiltonian for the host molecule at the site ip, hl, is the Hamiltonian for the guest molecule at 1 m, and V is an intermolecular interaction

term. Localized basis functions that span the problem and

that are appropriate for a deep trap system are com- prised of a crystal ground state

fig= % 1921 -Wlm-.V)h,N/h

and one-site excitation functions

(2)

(3)

(4)

where v/‘and @are wavefunctions for the rth and sth excited states of the guest and host molecules, respectively. It is convenient to take these @fp in linear com- bination as

(5)

to represent a state that correlates with the zero wavevector (optically accessible) level of a host crystal in which all band structure is washed out [ 16,17 1. The full crystal wavefunctions are linear combina- tions of these basis functions.

The lattice is assumed to be rigid with the guest oc- cupying a substitutional site. Accordingly, all wavefunctions may be classified by their behaviour under the site group (C,); the result is summarized in table 1. Interest here lies principally in crMM two-photon intensity so we focus on A, and B,, guest states and A, host states. Little is known about BZg and Bsu guest states or B, host states which presumably lie at high

A. Bree ami R. Zwarich I ~~erni~al Physrcs 170 (1993) i85- 192 187

Table 1 Correlation between the different electronic states of the guest anthracene molecule f D2,,) and the host carbazole or fluorene molecule (C,,) through the lattice site (C,)

Anthracene G&x)

Site symmetry CC.)

Carbazole (CZY)

LL, MM, NN A,

A‘f Bx, A’

A, LL, MM, NN h4

MN &s N %u

B, MN N

A, NL BI,

A5 NL

L bu A”

LM B, B2 LM L

energy; we neglect them. It follows from table 1 that symmetry will allow A, and B,, guest states to mix amongst themselves and with A, states of the host since these are all symmetric to the site operation od~oMF, and the indices r and s run over all such excited states. We emphasize that while anthracene is centred the host molecules, carbazole and fluorene, are not so that these host molecules do have a per- manent dipole moment in all electronic states.

We restrict attention to the dipole approximation in order to evaluate the elements of the energy matrix. It turns out, for example, that within this approximation the ground basis state can interact with all excited basis functions except those where the guest excitation has total symmetry. To evaluate these elements, the interaction potential is taken as a two- centre multiple expansion in which we retain only the dipole-dipole term. We see that the expressions re- duce to dipole-dipole sums (I) in which a static or transition moment at site jq interacts with a transition moment at site ip or lm, the sum being taken over all sitesjq in the lattice occupied by host molecules. The off-diagonal matrix elements will be of several types, such as

If”=

(9)

Here, for example, I *prg defines the interaction sum between the transition dipole moments ( rl IYE lg) on a guest molecule and a static dipole moment (g 1 m 1 g) on a host molecule in its ground electronic state.

It will prove useful to use a more specific indexing of the guest states. Hence, we replace the index r, for the guest molecule, by t for the specific target B,, state near 400 nm, by u for the next excited Bi, state and by u for the first excited A, electronic. state. We could extend the model to include sums over all u and v but the large energy denominators cause high energy states to have a smaller effect. Using this nomenclature, we find unno~alized crystal wavefun~tions, containing only first-order corrections, which have the form

@g=Qig-

(10)

(13)

@“= T@*+ _JFY_)L;m

+ -$$s $“-MY,. (14)

It is interesting to notice from eq. ( 12) that excited Ag states of anthracene do not mix with Ai states of the host molecules. This comes about because the

188 A. Bree and R. Zwurich ~ C~~icaI Physics I70 (1993) 185-192

transition moment (vi m 1 g) in the guest molecule vanishes.

It is now easy to derive expressions for transition dipole moments in the mixed crystal from the above wave functions if we set the dipole moment operator (M) in the crystal in terms of the molecular dipole operators (m) as M=Cim,, but it is convenient to restrict attention to a transition moment per molecule. We will consider only terms that are first order in a correction since the wavefunctions themselves include only first order corrections. The TPES tensor element is a sum of terms each having a product of two dipole moment elements in the numerator; it turns out that, for the centred molecule anthracene, one of these moments is allowed and the other is “induced”, involving a host static moment in state I g) , or Is), or both.

4. Results

The absorption spectrum of the first system of anthracene in a single crystal of carbazole at a nominal mode fraction of 3 x 1 0e5 is shown as fig. 1. The crystal was held at 1.8 K under liquid helium at reduced pressure. Only the spectrum polarized along the b crystal axis is shown; the a polarized spectrum has the same shape and a little less than half the intensity. A more accurate value for the mole fraction was ob- tained by dissolving an adjacent section of the crystal in solution and making use of the known molar ex-

origin

Fig. 1. The b-polarized absorption spectrum of anthracene in a carbazole crystal at 1.8 K.

tin&on coefficient of antracene in the solvent at room temperature; the error in this method is probably about 200/& The origin band, at 25 5 17 cm-‘, is the strongest band in the spectrum. There is a prominent phonon sideband which partially obscures the vibrational assignment but intervals of 393 and 139 1 cm- ’ are clearly seen.

The fluorescence spectrum of anthracene was detected using a gate interval of 15 ns. Ground state vibrational intervals of 398,622,794, I 172, 1266, 1407 and 1564 cm-’ were observed. The shape of the fluorescence spectrum was approximately the mirror image of absorption but with the 1266 and 1564 cm-’ intervals relatively stronger, so that the intensity distribution amongst the active vibrations is largely de- termined by Franck-Condon factors. The linear spectroscopy of anthracene is well understood. The absorption spectrum (see fig. 1) is shown here only to provide a direct comparison with the TPES.

Interestingly, the phosphorescence of the carbazole host was observed when the gated integrator was replaced by a standard dc photometer. Althou~ the two emission spectra (the fluorescence of anthracene and the phosphorescence of carbazole with its origin at 24 555 cm- ’ ) overlapped spectrally, they were completely separated using time discrimination in the detection system. The intensity ratio of the origin band of this phosphorescence was Z,: Zb: I,= 2.1: 1: 0.2. If the transition is assigned as ‘A, t ‘Ai then the pre- dominant out-of-plane character of the emission indicates that spin-orbit coupling favours the spin state crY either in intersystem crossing or in phosphorescence.

The two-photon excitation spectrum is shown in fig. 2. Only the (Z&f and (cc) pola~zations are given. Spectra in all other polarizations were much weaker and provide no extra information. The relative intensities tell us that only totally symmetric final states are reached. The two-photon forbidden but crystal- induced component is seen in the (bb) polarization. The origin band is no longer the strongest line in the spectrum; rather, the 0 + 139 1 line is far stronger. In this regard, the carbazole matrix shows a different behaviour from fluorene [7] where the origin is strongest. The vibrations at 393 and 1391 cm-’ are ap modes and appear in abso~tion through Condon effects. The origin and all the Condon allowed bands built upon it are forbidden in the two-photon spec-

A. Bree and R. Zwarich /Chemical Physics 170 (1993) 185-I 92 189

400 1

x .e m L a) !

Wavenumber

Fig. 2. The two-photon excitation spectrum of anthracene in a carbazole crystal at 1.8 K. Only the two strongest polarizations, (bb) and (cc) are shown. The numbers above the peaks represent vibrational intervals (in cm- ’ ) from the electronic origin.

trum of the free molecule and they appear in the mixed-crystal spectrum because of intermolecular interactions. The enhancement of 0+ 139 1 over the origin band must arise through a change in an energy denominator as the matrix is changed. Again, strong phonon sidebands are present in the spectrum and they have about the same intensity relative to the zero- phonon band as in the normal absorption spectrum in fig. 1.

The vibronically induced component of the two- photon spectrum is seen in (cc) polarization. The crystal-induced component is also observed in this polarization as seen by the presence of the origin. Vi- brations ofb,, symmetry that couple the B,, state with Ag states are easily seen 223, 648 and 892 cm-’ to the blue of the origin which, in turn, is red-shifted 458 cm-’ from its position in the fluorene matrix.

The next two-photon system is observed as two sharp bands at the edge of the host carbazole absorption at 29452 cm-’ [ 191. The first sharp line is at 29323 cm-’ with a second weaker line at 29364 cm-‘. This system, masked almost completely by the host absorption, has AB symmetry. Although it re- mains uncertain whether or not this refers to electronic or vibronic symmetry [ 7 1, we will provide in- direct evidence later to suggest that these states have

& vibronic symmetry. The relative intensities for the induced origin of the

anthracene B,,+-A, two-photon system and for the

Condon bands 0+ 393 and 0 + 139 1, as well as for the two vibronically induced false origins at 0+ 648 and 0 + 892, are given in table 2. Data for anthracene in fluorene crystals taken from ref. [ 71 are included. It is assumed that the vibronic component appears purely through an intramolecular effect and so should be the same for both the fluorene and carbazole matrices. With this in mind, we have scaled the intensities of all lines so that the intensity of the 0+648 (b,, vibration) is 1.0 in both matrices. The crystal- induced component arises from intermolecular interactions, of course, and the relative effectiveness of the two matrices can be directly compared in this way.

Intensities have been quoted as heights rather than areas because the presence of phonon sidebands complicates the separation of the vibronic bands. The values given are the means from all spectra measured on several different samples having different doping levels. The reproducibility was only about 15% even for the stronger lines (like the origin and 0 + 139 1) and was correspondingly worse for weaker lines (like

0+393). From table 2, it is evident that carbazole is more

effective than fluorene in inducing the two-photon spectrum. The enhancement factor ( Zcarbazole/ Z fluorene) increases from 6 at the origin, to 8 at 0 + 393 and to 29 at 0 + 139 1. The first short-axis transition in carbazole is at 29452 cm-’ while, in fluorene, it lies above 33000 cm-‘. The enhancement factor for the carbazole matrix increases as the vibronic band in anthracene nears in energy the short-axis absorption system in the matrix, and we see that the elec-

Table 2 Line heights observed in the two-photon excitation spectra of the anthracene molecule in either a carbazole or a fluorene matrix at 1.8 K. The intensities have been normalized so that the vibra- tionally induced line (0+ 648) has a height of 1.00. The enhancement quoted in the final column is the ratio IerJ I aUonnc for the crystal-induced lines only

Band Carbazole Fluorene Enhancement

(bb) (bb) (cc) (bb) (cc)

origin 5.0 1.0 0.87 0.00 6 0+393 2.6 0.33 0.33 0.00 8 o+ 1391 13.5 1.22 0.46 0.00 29 0+648 (1.00) (1.00) 0+892 0.68 0.75

190 A. Bree and R. Zwarich /Chemical Fhysm 170 (I 993) 185-192

tronic states of the matrix do play a role in the observation of the two-photon spectrum.

To account for these observations, the following model is used. The ‘BiUcl& transition is placed at 26700 cm-i with a transition length of 0.61 A using information from a solution spectrum. To account properly for the intensity enhancement, the origin and vibronic bands, placed at 0 + 400 and 0 + 1400, are treated as separate transitions with lengths of 0.29, 0.18 and 0.2 1 A, respectively. These intensities were measured from a photo~aphic absorption of anthracene in n-heptane at 4.2 I( taken in this laboratory by Katagiri [ 20 ] some years ago. The lowest-energy, h4- polarized transition in the hosts (with dipole transition lengths given in parentheses) are 29500 cm-’ (0.34 A) for carbazole and 36700 cm-’ (0.23 A) for fluorene. The approp~ate zero-wavevector Ewald dipole sums, calculated for a transition length of 1 A placed at the molecular centre of mass and parallel to the axis M, are - 22 14 and - 2844 cm-’ A2 for carbazole and fluorene, respectively. The static dipole moments were taken as 0.4 and 0.1 A for carbazole and fluorene.

5. Discussion

The key result from the TPBS of anthracene is the observation of enhanced intensity for a Condon progression as the vibronic state approaches energeti- cally closer to the host singlet A, state. This suggests that the mechanism that induces the intensity into the TPES must involve the energy term ( ws - w ’ ) - ‘. Inspection of eqs. ( 11) or ( i3) indicates that it is the mixing of states IS> and I t) that is signi~~ant for the crystal-induced effect.

However, there are two different ways that this mixing of states can bring about an intensity transfer into the two-photon spectrum. The first is just the method described by Craig and Thi~namachandr~ [ 161. Assuming that only the two states Is) and I t > mix, one gets the early result [ 16 ] that the transition dipole moment (A!$ ) per anthracene guest molecule in the crystal is

(15)

where rng refers to a transition moment in a host

molecule and the approximation sign implies that unnormalized wavefunctions have again been used. However, since the coefficient Fig/ ( ws--0’) is only 0.11 for the 0 -t 139 1 vibronic band of anthracene in carbazole, the largest value, the increase in intensity of this band from the oriented-gas value is only IO!, an intensity transfer to anthracene from the host transition that is too small to be detected in the absorption spectrum shown in fig. 1.

The situation is rather different for the two-photon spectrum of anthracene in the host matrices. Here, the tw~photon tensor can be written as

since the unpe~~rbed transition is forbidden. Again, a fraction [ f’a’g/ ( oS- 0’) ] * of the two-photon scattering off excited states to the final state Is) of the host molecule has appeared in the spectrum of the guest anthracene molecule. Now the transferred intensity is significant, although small, since the zero- order effect is forbidden. The excited states of the host involved in the scattering could have Ai, Bi or Bz symmetry yielding cont~butions to cyMM, a,.@$ and oLL, respectively, and al1 components can transfer to the guest molecule. The two-photon excitation spectrum of the carbazole Is> + lg> transition has been measured [ 19 ] and the observed ratio of intensities in each polarization is Zarr:Ibb:Icc=0.083: 1.00: 1.61. In fig. 2, some intensity is observed in the (cc) polarization at the origin band, it is also pronounced at the vibronic band 0+ 1400. Indeed, this is the only mechanism that can account for induced intensity in the (cc) polarization in the carbazole matrix.

If we divide the observed (cc) intensity by 1.6 1 and subtract from the ObSeNed (bb) intensities quoted for anthracene in carbazole in table I, we get residual values of 4.4, 2.3 and 12.6 for the intensities at the origin, 0 + 400 and 0 + 1400 which must be induced as pure (bb) polarized intensity by some other mechanism. Before we go on to discuss the second mechanism, it is worth noting that this first mechanism cannot be important for the fluorene matrix where there is negligible (cc) intensity at the origin.

The second mechanism involves the direct scattering off the crystal-corrected wave functions described in eqs. ( 10 )- ( 14 ). However, the residual induced intensities (i.e. after removal of intensity

Table 3

A. Bree and R. Zwarich /Chemical Physics 170 (I 993) 185-l 92 191

Calculated intensities for the TPES of anthracene as a guest molecule in carbazole or fluorene host lattices. The intensities have been scaled to match observed values at the origin band.

Band

origin 0+393 o+ 1391

Carbazole

mechanism 1

(0.62) 0.33 1.37

mechanism 2 total observed

(4.4) (5.0) 5.0 2.3 2.6 2.6 9.7 11.1 13.5

Fluorene

total

(0.87) 0.36 0.59

observed

0.87 0.33 0.46

induced by the first mechanism) also shows a strong enhancement as the host transition is approached. This implies that the energy term (w’--w’)-’ still plays a prominent role which, in turn, implies that it is scattering off the crystal state @“that is important. If the sum-over-states in the expression for the two- photon tensor is reduced to include only scattering off W, then one finds that the crystal-induced two- photon tensor for the guest is

(17)

where (ZJ~-Z$ ) is the change in the static dipole moment for the host molecule between the ground and excited electronic states. This contribution can only generate a contribution to (Ye,,,, since both static moments and rnz lie parallel to the Mmolecular axis.

The calculated TPES intensities for anthracene in the two host lattices, carbazole and fluorene, are summarized in table 3. These intensities have been arbitrarily scaled to match the observed values (also given in arbitrary units) at the origin band. For this reason, the intensities at the origin are enclosed in parentheses. In fact, it is not yet possible to calculate absolute intensities since we have no knowledge of ag (in model 1) or of (pg-pg) (in model 2). However, both models predict that the induced intensity scaled with [ Z”g*‘g/ ( os- of) I2 and so have the same dependence on the energy denominator.

It is important to notice that there is much less of an enhancement predicted along the vibrational progression for anthracene in the fluorene host matrix. The reason for this is that the energy difference ( os--0’) is large, and effectively constant in this case, for all the vibronic bands of anthracene considered. This prediction mimics the observations. Indeed, the relative intensities along the progression for the TPES

of anthracene in fluorene [ 71 is not much different from that observed in the regular absorption spectrum (seetig. 1).

These preliminary calculations were extended to include excited states other than just state Is) of the host matrix in the two-photon scattering process. An interesting case is to include an A, excited electronic state of the guest anthracene molecule at an energy of 29 400 cm-‘; an & state has been identified [ 71 near here but it was nuclear if the state was electronic or vibronic in nature. The modelling showed that if there was any significant dipole coupling between this new state and ]g) and 1 t), then the scattering off an A, electronic state here would dominate the TPES and this, in turn, suggests that the AB state is vibronic, representing a bz,, vibrational addition to a BzU electronic state.

6. Conclusion

The TPES of anthracene at 1.8 K held as guest molecule in a carbazole host matrix has been measured in the region of the ‘Blu+ ‘Aa low-energy transition. The pure two-photon transition is forbidden in the isolated molecule but it is induced in a lattice of polar molecules. The carbazole lattice, used here, is at least one order of magnitude more efficient than the fluorene lattice studied earlier [ 71. The enhancement arises both from the larger static dipole moment on the carbazole molecule and from the fact that the carbazole band structure lies at a lower energy than in fluorene and so couples more strongly through dipole forces with the upper electronic state of

anthracene. Organic crystals in which the molecules have a per-

manent dipole moment have been considered here for

192 A. Bree and R. Zwarich /Chemical Physics 170 {i 993) f&T-I 92

the first time from a theoretical point of view. There is no si~i~cant difference in the equations that are derived for the ordinary absorption spectrum and the treatment given by Craig and Thirunamachandran [ 16 ] in the deep trap limit continues to be applicable to these new systems. New features do appear in the theory for the two-photon absorption where the static dipole moment does play a role.

M~ell~~g carried out for the systems, anthracene in fluorene and anthracene in a carbazole host crystal, was able to predict two-photon intensities close to those observed. In carbazole, the intensity along a progression in a totally symmetric vibration in the guest anthracene molecule was enhanced by factors up to about 30-fold as the energy of the vibronic level approached in energy the first singlet level in the host crystal. The simple model developed here was able to account for this behaviour.

The authors are grateful for some very useful sug- gestions from Dr. T. Thimnamachandran concern- ing the details of the m~elling and also for financial support from the National Sciences and Engineering Research Council of Canada.

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Matrix-induced two-photon absorption in anthracene