The Triplet Excimer of Naphthalene: A Model System for Triplet−Triplet

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The Triplet Excimer of Naphthalene: A Model System for Triplet
Triplet Interactions and Its Spectral Properties Mathias Pabst,* Bernd Lunkenheimer, and Andreas K€ohn Institut f€ur Physikalische Chemie, Johannes Gutenberg-Universit€at Mainz, Jakob Welder-Weg 11, 55099 Mainz, Germany

bS Supporting Information ABSTRACT: Basic concepts of triplet excimer formation and triplet
triplet interactions between molecules with conjugated πsystems are investigated by means of ab initio quantum chemical calculations, employing the second-order coupled-cluster method CC2 and the second-order propagator method ADC(2). The naphthalene dimer turns out to be a very fruitful model system for which weak and strong electronic coupling can be identified depending on the mutual arrangement of the monomer moieties. From geometry optimizations in the excited state, we determine binding energies, including solvent effects, and transient absorption spectra. The most stable T1 conformation turns out to be a face-to-face arrangement with a rather short intermolecular distance. Its stabilization can be rationalized by a very strong electronic coupling due to a maximum overlap of the π-systems, which allows a strong admixture of charge-transfer configurations. Conformations without π
π-overlap show only a weak coupling and are less stable. The predicted transient Tn r T1 spectrum of the face-to-face dimer is in agreement with experimental observations for the triplet excimer, while all other considered conformations give rise to a transient spectrum, which closely resembles that of the monomer. In addition, we study the dependence of the triplet excitation manifold on the intermolecular distance, which yields valuable information on the nature of the triplet excited states in various conformations. The findings are likely to carry over to excimers of other aromatic molecules. We also investigate π-stacked naphthalene oligomers (up to the pentamer), which might be used as a model system for excimer formation and propagation in larger π-stacks. These can occur in amorphous layers of similar molecules, and the model may contribute to the understanding of the elementary processes in organic semiconductors.

1. INTRODUCTION Intermolecular interactions can be significantly altered if one of the molecules is in an electronically excited state. If this leads to a strong enhancement of the cohesive interaction between the two molecules, the supersystem consisting of the two molecules is denoted exciplex. Exciplexes of equal molecules are also called excimers. An example controversially discussed in the literature is the triplet excimer of naphthalene. The naphthalene triplet excimer is an interesting model system for two reasons. First, there exist many experimental1
18 and some theoretical3,19,20 works on this topic, but nevertheless, it seems that the triplet excimer formation is not yet fully understood. Second, the naphthalene triplet dimer shows, depending on its molecular conformation, the two extreme cases of strong and weak coupling with and without π
π-interactions between the monomers (vide infra). Intermediate cases also can be realized experimentally by covalently linked naphthalene molecules with a defined conformation.3,10
15,17,18 Hence, the naphthalene dimer in the first triplet excited state is a perfect model system for the investigation and understanding of triplet
triplet interactions between molecules with π-systems. Excimer formation is particularly important for the photoelectronic properties of molecules with large π-systems, which are often used as organic semiconductors in photoelectronic devices. r 2011 American Chemical Society

The device properties, however, may be considerably changed due to excimer formation. The behavior and photoelectronic properties of these systems are crucial for the design and understanding of organic light emitting diodes (OLEDs) and other organo-electronic devices.21
28 In this context, triplet excitons are particularly of interest as they play a key role in, for example, phosphorescent emitters. In the present work, we study the naphthalene triplet excimer employing the second-order coupled-cluster model CC2,29 and a related propagator method, ADC(2).30,31 To the best of our knowledge, this is the first theoretical study of triplet excimers using a coupled-cluster method and sufficiently large basis sets. In the following section, we introduce some simple models that are useful for characterizing molecular dimers. The methods applied in this work are described in section 3. After that, the results of our calculations are discussed in section 4, starting with a description of the electronic states in section 4.1 and a discussion of solvent effects in section 4.2. Then, the Tn r T1 absorption spectra are analyzed in section 4.3 followed by a characterization Received: January 26, 2011 Revised: March 16, 2011 Published: April 01, 2011 8335

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Figure 1. Schematic potential energy curves of the excited states of a molecular dimer. The X-axis is the combined antisymmetric relaxation coordinate of the two LE states; see the text. Left panel: A weak coupling V < λ/4 between the two diabatic states, with reorganization energy λ, causes a double minimum potential with an energy splitting of 2V (e.g., T-shaped naphthalene triplet dimer). Right panel: In case of a strong coupling V > λ/4, the double minimum turns into a broad single minimum (e.g., F2F naphthalene triplet excimer).

of the excited states in locally excited (LE) and charge-transfer (CT) states in section 4.4. Last, we investigate the triplet excited states of some model oligomers of naphthalene in section 4.5 before we conclude in section 5.

2. MODELS FOR MOLECULAR DIMERS In this chapter, we briefly summarize some concepts and the definition of quantities that are useful for the characterization of molecular dimers. For a detailed review see, for example, ref 32. For the characterization of systems with electronically coupled states, the reorganization energy λ and the electronic coupling V are the central quantities. In the absence of electronic coupling, we have two excited electronic states, |A*Bæ and |AB*æ, that is, either monomer A is excited or monomer B. These two states define a diabatic basis that will be the reference in the following. The corresponding potential energy curves are shown schematically in Figure 1. The X-axis of each of the subfigures is the combined relaxation coordinate of the two diabatic states 1/(21/2)(QA
QB), where QA is the relaxation coordinate of excited state |A*Bæ and QB is that of excited state |AB*æ. The reorganization energy λ is the energy that is released when, after vertical excitation from one diabatic state to the other, the system relaxes to the new equilibrium structure; see Figure 1. It consists of a relaxation on the ground state energy surface of the deexcited monomer and a relaxation on the excited state energy surface of the excited monomer. Assuming harmonic potentials, the energy of the intersection of the two diabatic potential curves is by λ/4 above the energy of the minima. In the presence of an interaction between the two states, we get a coupling potential V = ÆA*B|H|AB*æ, with H being the Hamiltonian. To a good approximation, V can be assumed to be a constant along the combined relaxation coordinate. In the adiabatic picture, the coupling leads to an avoided crossing. The minimum splitting of the two surfaces is then exactly twice as much as the value of the electronic coupling V. In the case of weak coupling, V < λ/4 (left panel of Figure 1), the energetically lower excited adiabatic state has a double minimum potential with a barrier of λ/4
V. In this case, the relaxation of molecular coordinates in the excited state causes symmetry breaking, and the excitation is localized on one of the

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monomers. At each minimum, the adiabatic electronic wave function is nearly identical to the respective diabatic wave function, and the picture of coupled LE states holds. For strongly coupled states with V > λ/4 (right panel of Figure 1), the double minimum potential is turned into a broad single minimum potential. In this case, the symmetry is not broken by the relaxation of the molecular coordinates, and the electronic excitation is delocalized over both monomers. Such strong couplings usually come about by strong admixture of CT states.33,34 Interactions between LE and CT states may change the spectral properties of the dimer considerably as compared to the corresponding monomer. To investigate the coupling pattern between LE and CT states in a dimer, it is very helpful to discuss the following four-state model, as advocated by Harcourt et al.33 Similar four state models were already employed for singlet excimers by Murrell and Tanaka,35 Azumi et al.,36,37 and Chandra and Lim.19 The Hamiltonian matrix may be written in the following form 0 1 βH βP ωLE V B C B V ωLE βP βH C C ð1Þ H¼B Bβ βP ωCT W C @ H A βH W ωCT βP The matrix elements are defined as ωLE ¼ ÆABjHjABæ ¼ ÆABjHjABæ

ð2Þ

V ¼ ÆABjHjABæ

ð3Þ

ωCT ¼ ÆA
Bþ jHjA
Bþ æ ¼ ÆAþ B
jHjAþ B
æ

ð4Þ

W ¼ ÆA
Bþ jHjAþ B
æ

ð5Þ

βH ¼ ÆABjHjA
Bþ æ ¼ ÆABjHjAþ B
æ

ð6Þ

βP ¼ ÆABjHjAþ B
æ ¼ ÆABjHjA
Bþ æ

ð7Þ

where |A*Bæ and |AB*æ are the diabatic LE states defined above and |AþB
æ and |A
Bþæ denote the two principal CT configurations. H is the Hamiltonian operator of the dimer and βH and βP are the hole and particle transfer parameters, respectively, which describe the coupling between the LE and the CT states. If the two monomers are related by a symmetry operation, the Hamiltonian matrix can be decoupled into subblocks of opposite parity 0 1 βH þ βP 0 0 ωþ LE B C B βH þ βP C ωþ 0 0 CT B C ð8Þ H¼B
βH
βP C 0 0 ωLE @ A 0 0 βH
β P ω
CT ( ( with ωLE = ωLE ( V and ωCT = ωCT ( W. The block structure of this decoupled Hamiltonian matrix and the coupling elements between LE and CT states βH ( βP can be used to explain the coupling pattern for the naphthalene triplet excimer as discussed in section 4.4.

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Figure 2. Arrangements of naphthalene dimers studied in this work.

3. COMPUTATIONAL DETAILS The second-order approximate coupled-cluster singles and doubles model CC2 is the most simple member of the coupled-cluster hierarchy that accounts for electron correlation.29 It treats correlation effects consistent through second-order perturbation theory and has the same formal O (N5) scaling as second-order Møller
Plesset perturbation theory (MP2). However, it also allows the treatment of excited states. A closely related method38 is the algebraic diagrammatic construction model through second-order ADC(2), a propagator method proposed by Schirmer30,31 in the 1980s. In the present work, ADC(2) is applied for geometry optimizations, because it is somewhat more cost-effective for this purpose than CC2. All CC2 and ADC(2) calculations were done with the RICC2 module of H€attig and co-workers,39,40 which is part of the TURBOMOLE program package.41 Dunning's correlation consistent basis sets cc-pVXZ42 [X = D, T] and the appropriate auxiliary basis sets43,44 were applied. In a few cases, the corresponding augmented basis sets aug-cc-pVXZ45 were employed, as well. Geometry optimizations of the excited states were carried out at the ADC(2)/cc-pVTZ level of theory. The ground state optimizations were done at the MP2 level with the same basis set. The triplet
triplet (Tn r T1) transition moments were calculated at the CC2/cc-pVTZ level of theory as implemented in the RICC2 module of TURBOMOLE.46 For this calculation, the optimized T1 structure was used. We also performed some calculations on the face-to-face dimer (vide infra) using Dunning's aug-cc-pVTZ basis at the carbon atoms [referred to as (aug)-cc-pVTZ] to test the influence of diffuse basis functions but found only small deviations. Because we do not need to describe very diffuse states as we compare our findings with experimental results measured in solution, the plain cc-pVTZ basis set should be sufficient. Numerical second derivatives were calculated using the NumForce script of TURBOMOLE. For the calculation of solvation effects, we employed the conductor-like screening model47 (COSMO). COSMO has been implemented in the RICC2 module of TURBOMOLE in a similar manner as described for the polarizable continuum model48 (PCM) in ref 49; that is, an iterative procedure is scheduled for the CC2 calculation until self-consistency between the solute charge density and the solvent response is achieved. This procedure is state-specific, which means solute and solvent density both depend on the observed state. As parameters for the COSMO calculations, we used 2.0 Å for the radius of the carbon atoms and 1.3 Å for the radius of hydrogen. The solvent radius is set to 1.3 Å. These parameters define the surface of the cavity in which the solute molecule is hosted. 4. RESULTS AND DISCUSSION In the late 1980s, there was a discussion in the literature about the existence of the naphthalene triplet excimer.1
9 Nowadays, many works support the formation of triplet excimers of dinaphthyl

compounds under various conditions.10
16,18,20 In the experimental work by Terazima, Cai, and Lim, covalently linked naphthalene dimers were studied using time-resolved electronparamagnetic resonance (TREPR), phosphorescence, and transient absorption measurements.16 From the interpretation of these spectra, they suggested that these compounds form triplet excimers. This led to the assumption that an L-shaped arrangement is the preferred orientation of the naphthalene triplet excimer. This assignment was then revised by East and Lim on the basis of semiempirical and ab initio quantumchemical calculations. They found that the naphthalene triplet excimer may adopt several configurations, but the F2F and crossed orientation (with the long axes perpendicular and the molecular planes parallel to each other) were suggested to be most stable.20 This was supported by a recent experimental study of Hashimoto and Yamaji,18 who claim to observe excimeric phosphorescence of nearly F2F arranged dinaphthylcompounds incorporated in zeolites. In the present work, we studied five different dimer conformations of naphthalene, which are sketched in Figure 2: • A face-to-face (F2F) dimer, which is also called eclipsed or parallel dimer. It has the molecular point group D2h. • A T-shaped dimer with the molecular point group C2v. The long axes of the molecules are parallel, and the short axes are perpendicular, reminding one of the shape of the letter T. • An L-shaped dimer whose long axes are parallel, and the short axes are perpendicular to each other and arranged as the letter L (in the following referred to as 90 L-shaped). The molecular point group is Cs. • An intermediate between the F2F and the 90 L-shaped dimer with an angle of approximately 50 between the short axes (in the following referred to as the 50 L-shaped dimer). The molecular point group is Cs. • A slipped-parallel dimer with inversion symmetry, where the planes of the monomers are parallel but slightly displaced. The F2F arrangement is expected to be well suited for dispersion force16 and has maximum π
π-overlap. In addition, it is known to be the structure of the singlet excimer,3 and it is suggested to be the most stable triplet excimer conformation.17,18,20 For the T-shaped conformation, we assume an optimal electrostatic interaction since the partially positively charged hydrogens of one moiety are close to the partially negatively charged π-system of the other.16 Many covalently linked dimers, for example, the Agosta dimer,50 are L-shaped with an angle of g90, which was determined by TREPR spectroscopy.16 The slipped-parallel arrangement was suggested to be the most stable ground state structure by CCSD(T) calculations.51 Other configurations, like, for example, the crossed dimer (with the long axes perpendicular and the molecular planes parallel to each other), were not accounted for, as the long axes of the molecules were found to be nearly parallel by a comparison of the emission characteristic of the naphthalene excimer and the Agosta dimer.3 8337

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Table 1. C
C Bond Distances (See Figure 3 for the Definitions of the Bond Lengths) of the S0 and T1 States of the Naphthalene Monomer and Its Dimers as Well as the Mutual Distances of the Monomer Moieties in Å (MP2/cc-pVTZ for the Ground State; ADC(2)/cc-pVTZ for Excited States)a arrangement monomer

Figure 3. Definitions of bond lengths and the distance between the monomer moieties in the naphthalene dimer.

D2h

state S0

ri

rmi

rmo

ro

δ

MC

1.43 1.41 1.38 1.41

S0

S0 (exp.b) 1.41 1.43 1.36 1.42 T1 (13B2u) 1.44 1.41 1.44 1.36

T1

face-to-face

D2h

T1 (13B3g) 1.44 1.41 1.41 1.38 3.08 D

T-shapedc

C2v

T1 (13B2)

(vertical)

1.43 1.41 1.38 1.41 4.83 S0

(horizontal) T-shapedd

4.1. Structures and Properties. In this section, we discuss the

structures and properties of the various conformations. According to the determined reorganization energy and electronic coupling, we assign the dimers to the strong and weak coupling case, as outlined in section 2. 4.1.1. Naphthalene Monomer. Characteristic for the D2h symmetric ground state, S0, is an equilibrium structure with a pronounced bond length alternation featuring a short bond between C2 and C3, rmo (see Figure 3 for the naming conventions), and a long bond between C3 and C30 , ro. In our calculations, we find rmo = 1.38 Å and ro = 1.41 Å, in fair agreement with the crystal structure of naphthalene (rmo = 1.36 Å, and ro = 1.42 Å).52 This pattern changes in the first excited triplet state, T1, which is also D2h symmetric but transforms according to B2u; the transition is thus polarized along the short axis of the molecule. Here, the calculated value rmo = 1.44 Å is pronouncedly longer than in the ground state, while ro = 1.36 Å is much shorter. Detailed information can be found in Table 1. These geometry parameters will serve as an indicator for the excitation character of the monomer entities in the optimized dimer structures. The vertical energy separation of T1 from the ground state is 3.27 eV. The adiabatic excitation energy is calculated to be 2.90 eV, which is in reasonable agreement with the experimental onset of the phosphorescence in solution at 2.65 eV53,54 and the 0
0 band of the phosphorescence excitation spectrum from a crystalline sample at 2.63 eV.55 As outlined in section 2, the reorganization energy λ is very important for the classification of the coupling strength in an excited dimer. For the naphthalene T1 state, we calculate an energy gain by 0.36 eV if the system relaxes from the vertical excitation point (with fixed S0 structure) to the T1 structure; in the S0 state, the energy difference between the vertical emission point (with fixed T1 structure) and the S0 structure is 0.37 eV. In total, the reorganization energy of the dimer in the T1 state amounts to λ = 0.73 eV. 4.1.2. Ground State Dimer. There are only a few spectroscopic measurements of the ground state dimer of naphthalene, and its structure has not yet been definitively determined by experimental results.56
59 However, there are a number of theoretical studies on this subject.51,60
65 The probably most accurate results were derived by Tsuzuki et al.,51 who applied an MP2 and CCSD(T) extrapolation scheme as an approximation for the complete basis set limit of the binding energy. Their calculations suggest that the slippedparallel arrangement is the most stable (counterpoise corrected binding energy of 0.25 eV at a distance of 3.9 Å). 4.1.3. Face-to-Face Excimer. Our calculations predict a D2h symmetric T1 state (13B3g) for the F2F dimer. As obvious from Table 1, the C
C bond distances are approximately the average of

symmetry

1.44 1.41 1.44 1.36 C2v

T1

T1 (13A1)

(vertical)

1.44 1.41 1.44 1.36 4.83 T1

(horizontal) L-shaped 50e

Cs

T1 (13A0 )

L-shaped 90e

Cs

T1 (13A0 )

1.43 1.41 1.38 1.41 S0 1.44 1.43 1.39 1.43 4.57 1.46 1.42 1.45 1.38 1.43 1.41 1.38 1.41 5.99 1.44 1.41 1.44 1.36

a

In the last column, the excitation characters of the monomer moieties (MC) are listed (S0, T1, and D for the monomer ground and T1 state and the delocalized dimer T1 geometry, respectively). b Values from the crystal structure of naphthalene; ref 52. c Excitation localized at horizontal monomer moiety. d Excitation localized at vertical monomer moiety. e No minimum, geometry optimization yields the face-to-face structure. See the text for details. This geometry was used for calculations of properties.

the monomer S0 and T1 values. The average mutual distance between the moieties is 3.08 Å, which is significantly shorter than twice the van der Waals radius of carbon (approximately 3.7 Å). As the optimized naphthalene moieties are not completely planar, the distance varies for different positions. The central carbon atoms (C1 in Figure 2) are separated by 3.08 Å, the C2 atoms by 3.04 Å, and the outermost carbon atoms C3 by 3.13 Å. The particularly strong attraction at the C2 position is caused by the increasing electron density between these carbon atoms, which can be seen from the T1 r S0 difference density (see Figure 4). A very similar picture was recently found for a model compound that is used to study excimer formation of biphenyls.66 The T1 state of that compound was as well delocalized over both moieties, and the average distance of the π-systems was 3.03 Å. The adiabatic excitation energy of the T1 state amounts to 2.54 eV from which one would predict a strong red shift of the phosphorescence onset by 0.36 eV in comparison to the monomer. However, the T1 state transforms as the B3g irreducible representation of D2h, whereas the selection rules for phosphorescence state that it must be contained in the direct product space of dipole moment and angular momentum, that is, one of B1u, B2u, B3u. Hence, the phosphorescence in the F2F dimer of naphthalene is symmetry forbidden,17 and it becomes clear why it has not been observed in perfectly parallel model systems like naphthalenophanes17,54 or parallel dimers in a rigid matrix.67 However, under conditions where deviations from the perfect sandwich structure are possible, excimer phosphorescence may be observed, sometimes perhaps together with monomer phosphorescence. Takemura et al.1,2 observed excimeric phosphorescence of naphthalene in solution starting at 2.4 eV, that is, 8338

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Table 2. Binding Energies (BEs) of the Naphthalene F2F and T-Shaped Dimer and the F2F Trimer and Tetramera arrangement

state

BE

BE[mono]

BSSE

cp-BE

cp-BE[mono]

face-to-face

S0

0.37

0.19

T-shaped

T1 S0

0.73 0.35

0.37 0.19

0.17

0.56

0.28

T1

0.35

0.19

0.08

0.27

0.14

0.34b

0.93b

0.31b

0.51b

1.23b

0.31b

dimer

trimer face-to-face

T1

1.27

face-to-face

T1

1.74

0.42 tetramer 0.43

a

Figure 4. Difference density FT1(r)
FS0 (r) of the F2F dimer in the T1 state. Blue indicates increased and red indicates decreased electron density in the T1 state as compared to the ground state.

a red shift of ca. 0.2 eV as compared to the monomer, which is in good agreement with our calculations. In addition, it was shown by these authors that the perfectly parallel model system of Chandross and Dempster67 does not show excimeric phosphorescence in a rigid matrix at 77 K but in solution at higher temperatures, where deviations from the parallel arrangement are possible.1,2 Recently, Hashimoto and Yamaji found excimeric phosphorescence for nearly F2F arranged dinaphthylcompounds incorporated in Tlþ-exchanged zeolithes.18 The counterpoise corrected binding energy of the F2F arranged triplet excimer of naphthalene is 0.56 eV at the CC2/ cc-pVTZ level of theory (see Table 2); in other words, the excited state dimer is much more strongly bound than the ground state dimer. This binding energy is strongly enhanced by resonances, that is, the electronic coupling V introduced in section 2. V can be calculated as half the splitting of T1 and T2 resulting in V = 0.44 eV. Because this value for the electronic coupling V is much larger than λ/4 = 0.18 eV, the F2F arranged naphthalene triplet excimer belongs to the strongly coupled case (right panel of Figure 1). This finding is consistent with the results of the geometry optimization of the F2F dimer where the D2h symmetry was retrieved during the optimization steps; that is, there is only one minimum, and the excitation is delocalized over the two monomer moieties. The delocalization of the excitation can be visualized by the T1 r S0 difference density (see Figure 4) where we see changes in the electron density all over the molecule as well as between the monomer moieties due to the strong coupling caused by π
π-interactions. As an aside to this paragraph, we notice that for a correct treatment of intermolecular interactions, diffuse basis functions often are expected to be essential. We therefore also performed some calculations in which the cc-pVTZ basis set was extended by additional diffuse functions, cf. section 3. However, the results turn out to be very similar to the results that we reported above employing the cc-pVTZ basis. We thus believe that the cc-pVTZ basis is sufficient for the treatment of the naphthalene excimer.

The BEs per monomer unit (BE[mono]) are also given, followed by the basis set superposition errors (BSSE) and counterpoise (cp) corrected values for the BEs (cp-BE, cp-BE[mono]). All calculations were performed at the CC2/cc-pVTZ level. The values are given in eV. b This value is estimated from the BSSE of the F2F dimer.

4.1.4. T-Shaped Excimer. The above findings for the F2F dimer differ considerably from the results for the T1 state of the T-shaped dimer. Here, we obtain two minima that are almost degenerate (ΔE