Electronic Excitation of Polyfluorenes: A Theoretical Study - The

Apr 29, 2006 - We present systematic, theoretical investigations on structure−property correlations in polyfluorenes (PFs) derived mainly from the c...
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J. Phys. Chem. B 2006, 110, 9908-9915

Electronic Excitation of Polyfluorenes: A Theoretical Study WanZhen Liang,* Yi Zhao,* Jin Sun, Jian Song, Shuanglin Hu, and Jinlong Yang Hefei National Laboratory for Physical Science at Microscale and Department of Chemical Physics, UniVersity of Science and Technology of China, Hefei 230026, People’s Republic of China ReceiVed: December 12, 2005; In Final Form: March 23, 2006

We present systematic, theoretical investigations on structure-property correlations in polyfluorenes (PFs) derived mainly from the chain morphology, oligomer length, and chemical substitutent. Both the vertical absorptions and the vibrational contributions to electronic absorption and fluorescence spectra have been calculated. The effect of temperature on the nature of photoexcitations of PFs has been demonstrated. It is found that the vibronic (electronic and vibrational) structures of PFs are morphology-dependent. β-phase oligofluorenes (β-(FL)n) and ladder-type poly(p-phenylene) (LPPP) oligomers show a red shift compared to the spectra of R-(FL)n. The asymmetry of the absorption and fluorescence spectra in R-(FL)n and the fluorenone (FLO) defect oligofluorenes R-(FL)n-m(FLO)m is significantly more pronounced than that in planarized β-(FL)n and LPPP oligomers. By properly taking into account the anharmonic torsion potentials resulting from the strong electronic and nuclear coupling in the oligofluorenes, we have reasonably reproduced the experimentally observed spectroscopic features. The low-energy on-chain chemical defect sites such as FLO units act as charge-trapping sites for singlet excitations, are the predominantly lighting-emitting species, and thus alter the blue light-emitting properties of PFs whereas the blue-light-emitting properties of PFs are hardly influenced by the hole-transporting molecules. The optical properties of PFs have been predicted by the finite-size calculations. Energy gaps of PFs are estimated by extrapolations from excitation energies of oligofluorenes up to 21 FL units.

1. Introduction Conducting polymers are the most recent generation of polymers.1 They offer a unique combination of properties not available from any other known materials and have been used to manufacture promising thin film devices such as organic lightemitting diodes, organic solar cell, and organic field-effect transistors. Polyfluorene (PF) is a particularly prominent class of materials for light-emitting diode applications and as a host material for internal color conversion owing to its highly efficient blue emission and large energy gap.2-9 It has been shown to exhibit a complex morphological behavior that complicates its structure-property relationships. In the condensed state, PFs can undergo a conformation change during transitions.9 Both the twisted (in R-phase) and the planar (in β-phase) chain conformations have been observed.9-11 Several chemical modifications to the PF chain have been developed. For example, ladder-type poly(p-phenylene) (LPPP) is considered a variety of PF; highly localized oxidative emission species have also been detected.9,12 Currently, understanding the complex photophysical properties of fluorene-based materials has become an active area of research9-17 due to the complexity of emissions and the apparent sensitivity to processing conditions. Low-temperature optical spectroscopy measurements9-11,13,14 have demonstrated that the spectroscopic properties of R-phase PFs and β-phase PFs differ characteristically from one another in energy, line-width, and intensity. The π f π* transition of the R-phase PF is featureless, with a maximum at 3.23 eV, while the β-phase PF shows a narrow, well-resolved absorption peak at 2.84 eV and associated * Corresponding authors. E-mail: [email protected]; yizhao@ ustc.edu.cn.

vibrational progressions (VPs) superimposed upon the bulk absorption. Moreover, the normal synthetic procedure leads to incorporation of a small amount of chemical impurities which alter emission characteristics of PFs.9 In their pristine states, PFs emit bright blue light. During operation, however, an additional low-energy emission band around 2.2-2.4 eV appears. It has been attributed to the formation of fluorenone (FLO) groups, which are introduced by photooxidization, thermal oxidation, or during device fabrication.9-17 A few attempts15,18-22 have been made to chemically modify PFs in order to increase the device efficiency, such as, capping the OF chain with hole-transporting molecules (HTMs).20-23 Theoretical investigations are necessary since they can gain a deeper insight into the impact of chemical defect, morphological behavior, oligomer length, and the coupling strength between electronic and vibrational degrees of freedom on the nature of photoexcitations in the fluorene-based materials. So far some theoretical research24-30 has been focused on the electronic excitations of PFs by using the time-dependent density functional theory (TDDFT) or the restricted configuration interaction singles (CIS) implemented at the semiempirical Hamiltonian or Hartree-Fock (HF) theory level. Finite-size oligofluorenes (OFLs) with two to five FL units were used in the calculations, and the vertical excitation energies were evaluated. In fact, the vertical excitation energies are not experimentally observed ones since the experimental absorption or emission spectra are often vibrationally resolved. To have a meaningful comparison with experiment, we have to properly take into account the nuclear motion and the vibronic coupling. Besides, the oligomer, which includes only a few FL units, is too short to access the converged optical properties of the long polymer since PF can have molecular weights of hundreds of thousands, comprising

10.1021/jp0572481 CCC: $33.50 © 2006 American Chemical Society Published on Web 04/29/2006

Electronic Excitation of Polyfluorenes thousands of repeat units. It is interesting and necessary for us to study how the molecular properties evolve with increasing the oligomer length31,32 and study model oligomeric compounds with the different finite sizes to establish the critical oligomer length for which absorption and emission spectra correspond to the polymeric analogue.33 Furthermore, it is more appropriate to adopt the reliable theoretical modes which do not have empirical fits with experimental data to calculate both the absorption and emission spectra. In this work we apply reliable quantum chemical techniques to investigate the optical properties of PFs as a function of the oligomer length, chemical substitutent, chain morphology, or temperature and try to understand the natrure of the collective excitons and their dynamics as well. Both the defect-free and chemical defect oligomers are adopted, and the structureproperty relationships for oligomers will be established to rationalize the properties of high molecular weight linear π-conjugated polymers. A series of calculations are performed by varying the system size from very short oligomer to very long polymer. The effective conjugation length of the polymer will thus be estimated. The evolution of optical absorption profiles as increasing the system sizes will therefore be demonstrated. Since the defect-free and chemical defect chains are comparatively investigated, we thus observe how the optical properties of pristine PF chains change when systems bearing fluorenone (FLO) substitutents or HTMs, such as, N,N-bis(4methylphenyl)-N-phenylamine (MPA), as end groups and investigate the excited-state effects induced by FLO defects or MPA end cappers. To investigate the effects of unclear motion and vibronic coupling, we evaluate the vibrational contributions to electronic absorption and emission spectra. A clear relation will be established between the strongly anharmonic torsion potentials for FL/FLO liberations around the long molecular axis and the observed deviation from the symmetry of absorption and fluorescence spectra. The paper is arranged as follows: section 2 shows the theoretical methods by which our results are obtained. Section 3 presents the theoretical results and result analysis. Conclusions are given in section 4. 2. Theoretical Models 2.1. Vertical Absorption Spectra. We evaluate the optical absorption spectra of OFs based on the localized density matrix (LDM) method which has been developed to evaluate the excited-state properties of very large systems.34-37 The LDM method was developed within the time-dependent Hartree-Fock (TDHF) theory framework and used the localized properties of the reduced one-electron density matrixes. It is a general theory and has been employed at the semiempirical Hamiltonian and density functional theory level38 to investigate the optical properties of all-carbon materials. Some interesting results have been obtained. The optical properties of carbon chains, polyynes, and cumulenes have been systematically investigated by TDDFT with commonly used exchange-correlation kernels.39 It is found that TDHF approach leads to the best agreement with the experimental energies and all other approaches result in excitation energies which are too low or too high.39 Thus, it is appropriate for us to use TDHF to evaluate the optical properties of one-dimensional systems. Here we employ our LDM at the semiempirical intermediate neglect of differential overlap (INDO/S) Hamiltonian level.40 2.2. Vibrationally Resolved Optical Absorption and Emission Spectra. It is well-known that vibrationally resolved absorption and emission spectroscopies are related to the

J. Phys. Chem. B, Vol. 110, No. 20, 2006 9909 dipole-dipole autocorrelation function

C(t) )

Tr[e-βHeiHt/pµe-iHt/pµ] Tr[e-βH]

(1)

Here β ) 1/kbT, Tr(...) represents the trace over nuclear and electronic degrees of freedom, and µ is transition-dipole operator

µ ) |g〉µge〈e| + |e〉µegg|

(2)

In the Born-Oppenheimer approximation, the total Hamiltonian for two electronic states |g〉 and |e〉 can be written as

H ) |g〉Hg〈g| + |e〉He〈e|

(3)

where Hg and He denote the nuclear Hamiltonians of electronic ground and excited states, respectively. For linear response spectroscopy, eq 1 explicitly gives two correlation functions, Ca(t) and Ce(t) as

Ca(t) )

Tr[e-βHgeiHgt/pµe-iHet/pµ] Tr[e-βHg]

(4)

and

Ce(t) )

Tr[e- βHeeiHet/pµe-iHgt/pµ] Tr[e-βHe]

(5)

Here subscripts “a” and “e” correspond to absorption and emission, respectively. Thus, the optical absorption cross section R(ω) and emission cross section β(ω) are separately obtained from

∫-∞∞ dt exp(iωt - γ|t|)Ca(t)

(6)

∫-∞∞ dt exp(-iωt - γ|t|)Ce(t)

(7)

R(ω) ∝ ω and

β(ω) ∝ ω3

Here γ represents the dephasing factor. Because of the similar behaviors of Ca(t) and Ce(t), we only provide detailed evaluation of Ca(t) in the following. Consider a system with vibrational frequency changes and Duschinsky rotation on two electronic states. Under harmonic potential approximation, we write the Hamiltonians as n

∑i ωgi (pg2i + qg2i )

(8)

∑i ωei (pe2i + qe2i ) + ωeg

(9)

Hhg(q) ) 1/2 n

Hhe (q) ) 1/2

Here ωeg is the potential energy minimum difference between two electronic states with the zero-point energy correction. ωg and ωe denote the vibrational frequencies of electronic ground and excited states, respectively. The dimensionless nuclear coordinates qg and qe are related by

qe ) Sqg + D

(10)

where D is the displacement between the equilibrium configurations of two electronic states and S is the Dushinsky rotation matrix which allows the ground state and the excited state to have different coordinate systems. When the momenta and

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positions of the nuclei change very little upon photoexcitation, the intensities of vibrationally resolved electronic absorption or emission spectra can be calculated according to the FranckCondon (FC) principle. Under Condon approximation, the correlation function Cha (t) has an exact solution with Green’s function approach.41 The detailed expressions have been given in eqs 32 and 33 of ref 41. We use those formulas in this work. There are many alternatives for the calculation of Cha (t), such as the one in ref 42. 2.3. Effect of the Chain Torsional Motion on Electronic Excitations of Oligofluorenes. Because of strong electronphonon coupling, organic π-conjugated molecules are subject to structural distortions upon photoexcitation. The oligofluorene may twist from a nonplanar S0 equilibrium geometry to a nearly planar S1 equilibrium geometry. Due to the periodic torsion potential energy surface (PES) and the large difference between the optimized torsion angles of two states, harmonic approximation for the torsion PES becomes invalid. In this case, a method which is beyond harmonic approximation including anharmonic effects must be exploited. In this work we use a method proposed by Seidner et al.43 and used popularly by others44-47 to describe the torsional motion. If the coupling among the harmonic and anharmonic oscillators is weak or these oscillators have different time scale, we can decompose the nuclear Hamiltonian into two parts

H ) H h + Ht

(11)

where Hh is the Hamiltonian describing all the vibrational motions under the harmonic approximation and Ht represents one for the torsional motion. The Hamiltonians for the torsional motion of two electronic states can be separately written as

Htg ) -

p 2 ∂2 + Vg(φ) 2It ∂2φ

(12)

Hte ) -

p 2 ∂2 + Ve(φ) 2It ∂2φ

(13)

Here, φ corresponds to the torsion angle, It is a reduced moment of inertia, and Vg(φ) and Ve(φ) are the torsion PES of S0 and S1, respectively. In this case, the dipole correlation function eq 4 can be factorized into a product

Ca(t) ) Cta(t)Cha (t)

(14)

where Cha (t) has been given in ref 41 and Cta(t), which corresponds to the torsional motion, can be written as

Cta(t) ) 1/Zt Tr[e-βHg µgeeiHe t/pµege-iHg t/p] t

t

t

(15)

where Zt is the ground-state partition function. Equation 15 can be easily implemented numerically. To evaluate eq 15, we assume

Htg ξig(φ) ) Eig ξig(φ)

(16)

Hte ξie(φ) ) Eie ξie(φ)

(17)

Equation 15 is readily expressed as

Ct(t) ) 1/Zt

∑i ∑j 〈ξig|µge|ξje〉〈ξje|µeg|ξig〉e-βE +i(E -E )t/p i

g

j

e

i

g

(18)

Figure 1. VAS of (FL)6 with different chain conformations.

In the evaluation of eq 16 and eq 17, the discretized variable representation is built by the sinc function. 3. Results and Discussion 3.1. Vertical Absorption Spectra (VAS). We used finitesize oligomers to calculate VAS. The optimal ground-state geometries are adopted for the excited-state calculations here. The electric field is assumed to polarize along the long oligomer axis and the dephasing factor sets to 0.1 eV. The calculated VAS clearly show that the oligomer length, intramolecular π-conjugation condition, and chemical substitutent play an important role on the optical properties of OFs (see Figures 1, 2, and 3). 3.1.1. Spectral Changes: Effect of the Chain Morphology. A single PF chain is known to have three distinctive chain morphologies: the planar chain (β-(FL)n), the twisted chain (R(FL)n), and LPPP. Our goal is to discuss, from a theoretical standpoint, how the chain conformations of PFs influence their electronic structures. The calculations are performed for three OFs: R-(FL)6, β-(FL)6, and (LPPP)6. All the oligomers include six repeated FL units. (The FL block is a rigid biphenyl unit, bridged by a nonconjugated (sp3) carbon atom.) All the geometries are optimized at the B3LYP/6-31G(d) level with no point-group symmetry imposed. (For the geometries of three oligomers, see the inset of Figure 1.) For R-(FL)6, B3LYP/631G(d) predicts an average fluorene-fluorene torsion angle of 37.1° (out-of-plane angle), which agrees with the experimental value of ∼36°.9 Figure 1 shows that the spectral profiles of three OFs are qualitatively similar. Two strong absorption bands centered at around 3.2 and 5.2 eV are observed in all the oligomers. The observable discrepancy is that β-(FL)6 and (LPPP)6 show a slight red shift compared to the spectra of R-(FL)6. It is well-known that π -electron conjugation of organic molecules affects the locations and intensities of optical absorptions peaks. The discrepancy among VAS of three systems reveals that the intramolecular conjugation conditions of three systems may be different. With increasing π-conjugations, the low-energy modes red shift and their absorption intensities increase. The absorption spectroscopy measurements have shown that the β-phase OFs and LPPP oligomers have more extended conjugation than the glassy phase OF. The chain disorder in R-phase OFs shorten the effective conjugation length of π-conjugated PFs.48 As a consequence, excited states of β-(FL)6 have lower excitation energies and higher polarizabilities than those of R-(FL)6. 3.1.2. Spectral Changes: Effect of the Oligomer Length. Second, we consider how the spectral profiles evolve with increasing the oligomer length. The optical absorption spectra of a series of OFs with different system sizes are evaluated. For short oligomer, it is shown that the oligomer length plays

Electronic Excitation of Polyfluorenes

Figure 2. The optical gap vs 1/N.

Figure 3. VAS of FLO-end-caped and MPA-end-caped R-phase oligofluorenes. The spectra of FLO and MPA monomers are shown for comparison.

an important role on its electronic structure. The energies of the optical transitions in absorptions initially decrease and the overall absorption spectral profiles red shift with the reciprocal number of repeat units. The trend is similar to these reported experimentally for OFs.31,32,49-51 The red shift trend can be explained by the collective character of the exciton in terms of the single electron-hole excitation picture. As the oligomer-length continuously increases, the optical gaps finally saturate. The saturated optical gap can be obtained by plotting the optical gap via 1/N, where N is the number of carbon atoms. The saturated value corresponds to N f ∞. Figure 2 shows that the optical gaps Eg of R-phase PFs, β-phase PFs, and LPPP approach to 3.11, 2.92, and 2.82 eV as the oligomer length approaches infinity, respectively. The optical-gap values agree exactly with the locations of most intense peaks in the experimentally observed absorption spectra.9,14,16,17 No obvious change of the spectral profile is observed as the system size increases from 5 FL units to 21 FL units. Thus, the spectral profile of OFs with 21 FL units should correspond to the saturated profile of PFs. 3.1.3. Spectral Changes: Effect of Chemical Substitutents. Third, we consider how the one-chain chemical substitutents influence the electronic structures and optical properties of PFs. An oligomer with four repeat FL units end capped separately by hydrogens, FLO, or MPA is used in the calculations. The geometries together with the calculated absorption spectra are shown in Figure 3. Except for two strong absorption bands centered at ∼3.2 and 5.2 eV, additional low-energy bands centered at around 2.9 and 4.5 eV appear on the optical spectra of FLO-end-capped oligomer ((FLO)(FL)4(FLO)). The lowest peak corresponds to HOMO f LUMO transition and results mainly from a combination of local excitations from FL units to FLO defects (see the Supporting Information). This low-energy mode thus

J. Phys. Chem. B, Vol. 110, No. 20, 2006 9911 possesses a pronounced charge-transfer character, which corresponds to the charge-transfer state where the electron transfers from FL units to FLO defects. With respect to the ground-state Mulliken atomic charges in (FLO)(FL)4(FLO), we find that 0.12 electrons are transferred from four FL units to FLO end cappers. Table 1 shows the lower-lying singlet and triplet energies of R-(FL)6 and FLO monomer. The lowest singlet excitation energy of FLO is slightly lower than that of R-(FL)6. The fro¨ster energy transfer from FL backbone to FLO defects occurs, which localizes the excitons on the low-energy FLO sites. FLO defects thus act as guest sites for exciton recombination and are expected to be the predominantly emitting species, which explains why an additional low-energy band appears in PL emission spectra of FLO defect PFs. Except for additional low-energy bands induced by the on-chain FLO defects, other excitation modes are hardly influenced since these energy states are still come from the electron-hole pairs along the R-(FL)4 backbone. Comparing VAS of (MPA)(FL)4(MPA) with that of Hterminated oligomer (FL)4, we observe that the first absorption peak of (MPA)(FL)4(MPA) has lower transition energy and larger peak intensity than that of (FL)4. This substantial red shift of the absorption maxima can be attributed to electron donation of MPA groups, enlarging the effective conjugation length of (FL)4. The absorption peak intensities of (MPA)(FL)4(MPA) are comparable with these of (FL)6, and no explicit absorptionprofile change is observed in the low-energy range (E e 6.0 eV). The electronic wave functions of HOMO-1 and HOMO have been shown to be located on MPA end cappers while these of LUMO and LUMO+1 are located on FL units from our calculations (see the Supporting Information). The ground-state Mulliken atomic charges in (MPA)(FL)4(MPA) reveal that 0.02 electrons are transferred from MPA end cappers to four FL units. MPA end capper acts as a HTM, which hardly influences the electronic structures and optical properties of PFs but may balance the hole and electron currents in PF matrix and thus improve the device efficiency since the hole mobility is typically much greater than the electron mobility in FL-based materials which gives rise to more rapid polymer degradation. 3.2. Vibrational Progressions (VPs) within Electronic Absorption and Emission Bands. To have more close comparison with experimental spectroscopies and show how the changes in the equilibrium geometries of two electronic states, S0 and S1, influence VPs within electronic absorption and emission bands, we present a systematic study of vibronic coupling to electronic transitions at different temperatures. The absorption and fluorescence spectra of polyatomic molecules R-(FL)2, β-(FL)2, (LPPP)2, and R-(FL)(FLO) will be calculated. We have combined several computational approaches in this work. S0 equilibrium geometries, normal coordinates, and vibrational frequencies are calculated within the HF/6-31G(d) approximation. S1 energies, equilibrium geometries, normal coordinates, and vibrational frequencies are computed at RCIS/ 6-31G(d) theory level. These calculations are performed with the GAUSSIAN 03 program package.52 The results at the TDDFT level come from the TURBOMOLE package.53 The B3LYP exchange-correlation functional and SV(P) basis set are utilized with TURBOMOLE. SV(P) basis set is comparable with that of the 6-31G(d) one. The calculated vibrational frequencies are scaled by a factor of 0.89. 3.2.1. β-(FL)2 and (LPPP)2. Figure 4 shows the calculated absorption and fluorescence spectra of the planarized β-(FL)2 and (LPPP)2 at different temperatures. The damping factor γ ) 150 cm-1 is used. To have a close comparison with the experimental measurements, we set E0-0 ) 2.9 eV for β-(FL)2

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TABLE 1: The Lower-Lying Singlet (S) and Triplet (T) Excitation Energies of Oligomers and FLO or MPA Monomer (eV) molecules

B3LYP/6-31G** (S)

LDA

(FL)6 FLO MPA (FLO)(FL)6(FLO) (MPA)(FL)6(MPA)

3.20 (4.65) 3.13 (0.0), 3.19 (0.004) 3.91 (0.01)

3.23 3.09 3.83 2.94, 3.23 3.20

and E0-0 ) 2.8 eV for (LPPP)2, which are close to the saturated lowest vertical excitation energies of β-phase PFs and LPPP. (E0-0 is the minima energy difference between S1 and S0.) The optical spectra of planarized β-phase OFs and LPPP oligomers are strikingly similar. They both show a narrow, wellresolved absorption peak at 2.83 and 2.72 eV, respectively. Three to four vibronic maxima are observed within absorption and emission spectra. At the temperature T ) 110 K, the absorption and fluorescence spectra of β-(FL)2 and (LPPP)2 are displaced by only 0.11 eV relative to one another and have similar VPs. The most intense peaks in the absorption spectra are the second bands which would correspond to the “vertical transition”; i.e., during the electronic transitions, the nuclei were frozen at S0 equilibrium geometries. Comparing the spectra of β-(FL)2 and (LPPP)2 with the experimentally spectroscopies of PFs,9 we find that the relative intensities of 0-0 transitions in the spectra of β-(FL)2 and (LPPP)2 are weaker than those in polymers. This may reveal the facts that a greater change in bond length upon excitation takes place in the equilibrium geometries of β-(FL)2 and (LPPP)2 than those of polymers. Figure 1 in the Supporting Information shows the equilibrium geometries of β-(FL)2 and β-(FL)3 at S0 and S1. We observe that the bond-length difference between S0 and S1 of β-(FL)2 is larger than that of β-(FL)3. It is well-known that the larger the shift in bond length between S0 and S1, the higher the value of Vvert, and smaller the overlap of the V′′ ) 0 and V′ ) 0 vibrational states. Here double-primed and singleprimed symbols are used for S0 and S1, respectively. It has been experimentally found that both the spectral positions and relative intensities of 0-0, 0-1, and 0-2 transitions change with increasing the number of repeated FL units and the relative and absolute intensity of 0-0 transition increases with increasing

Figure 4. Absorption and fluorescence spectra of the planarized β-(FL)2 and (LPPP)2 at different temperatures.

B3LYP/6-31G** (T1) 2.49 (0.0) 3.18 (0.0)

expt 3.2-3.3 3.27 (S2)

the oligomer length.31 We may thus conclude that OFs with two FL units are too short to access the converged optical properties of the long polymer. β-(FL)2 and (LPPP)2 show negligible 0-0 energy gaps within the emission and absorption spectra. At T ) 110 K, they are only 9.9 and 12.5 meV, respectively. As the temperature increases to 300 K, they separately increase to 34.2 and 37.2 meV. The effect of the temperatures on peak intensity distributions is appreciable. As the temperature changes, an explicit redistribution of peak intensities within VP of emission and absorption spectra is observed. The peak amplitudes of vibrational transitions decrease. At lower temperature, the most intense peak in VP of emission spectra is 0-0 lines, which correspond to the download vertical transition, from V′ ) 0 to V′′ ) Vvert ) 0 and arise from mostly the lowest excitation state and not from thermally activated excitations. The intensity of the 0-0 line is most sensitive to changes in the excitation coherence volume due to thermal scattering into other excitation states, and it decreases with increasing temperature. When temperature increases, the higher vibrational energy levels are populated. Thus, the relative peak intensities of 0-1 or 0-2 lines may increases as compared to 0-0 lines. 3.2.2. Torsion Potential Energy Curves. The geometric and electronic structures of R-(FL)n that resulted from the conjugated backbones are nearly identical with (LPPP)n and β-(FL)n. The distinctive difference is that FL units in R-(FL)n are able to liberate around the long molecular axis while (LPPP)n and β-(FL)n oligomers remain rigidly planar as promoted to the excited state. Geometry optimization reveals that the conformation of R-(FL)n and R-(FL)(FLO) twists from the nonplanarity in S0 to near planarity in S1. The large difference between the central dihedral torsion angles of S0 and S1 will lead to significantly different Born-Oppenheimer potential energy curves and definitely influence the features of electronic spectra. Figure 5 shows the adiabatic torsion potential energy curves of R-(FL)2 via the torsional vibrational normal coordinate φ (the dihedral angle among atoms 1, 2, 3, and 4). The potentials in S0 and S1 of R-(FL)2 have been computed on a 5° grid in the interval [-90°, 90°] assuming alternating signs for the interring tilt angle. For the ground state of R-(FL)2, we find a W-shaped, double-well potential with its minima at ∼45° by HF/6-31G(d) calculation and ∼37.6° by B3LYP/6-31G(d) calculation. The potential curve obtained by B3LYP/6-31G(d) is closer to the experimental measurement than that by HF/631G(d). B3LYP/6-31G(d) double-well potential for the ground state features a lower energy barrier at φ ) 0° inter-ring tilt angle (0.075 eV) than that at φ ) 90° (∼0.12 eV) and the energy minima are closer to the experimentally determined values. The excited-state torsion potentials of R-(FL)2 predicted by both CIS and TDDFT are nearly U shaped and almost parabolic. CIS gives an energy minimum at 8.1° while TDDFT produces an energy minimum at 7.4°. The excited-state torsion potentials exhibit much higher flanks than the ground-state potentials, rendering them less susceptible to influence from the surroundings. CIS predicts much larger excitation energies than TDDFT (see Figure 5).

Electronic Excitation of Polyfluorenes

Figure 5. Torsion potentials of R-(FL)2 and R-(FL)(FLO).

When one of two FL units is replaced by a FLO unit, interestingly, the S1 potential curve changes drastically while the ground-state potential curve does not change much as compared with R-(FL)2 (see Figure 5). The energies of R-(FL)(FLO) in the S1 state are appreciably lower than those of R-(FL)2 since the first excited state of R-(FL)(FLO) corresponds to the electron-transfer state. TDDFT also predicts an explicit double well potential in the S1 state of R-(FL)(FLO). The S0 energy minimum is at φ ) 36.5°, while the S1 energy minimum is at φ ) 20.9°. 3.2.3. r-(FL)2 and r-(FL)(FLO)2. In the calculations of absorption and fluorescence line shapes of R-(FL)2 and R-(FL)(FLO), the potentials of S0 and S1 produced separately by DFT and TDDFT have been used. However, the equilibrium geometries, normal coordinates, and vibrational frequencies of the ground state and excited state are still calculated at HF/6-31G(d) and CIS/6-31G(d) theory levels, respectively. Figure 6 shows the calculated absorption and fluorescence spectra of R-(FL)2 at different temperatures. It is found that the absorption begins at 2.8 eV and reaches a maximum at 3.24 eV. At ambient temperature, the absorption band that resulted from π-π* transition is featureless while the PL emissions of R-(FL)2 exhibit clear well-resolved vibronic features with bands at 2.90, 2.70, and 2.54 eV, which may be assigned to the 0-0, 0-1 and 0-2 intrachain singlet transitions. It is explicit that the low-energy torsional motion between FL units severely break down the symmetry between absorption and emission spectra. By properly taking into account the low-energy torsional motion, we reproduce the experimentally observed spectral profiles of a FL dimer.31 Here we set E0-0 ) 3.05 eV and γ ) 110 cm-1. The experimental spectra of a FL dimer31 are red shifted 0.55 eV to compare with these of PFs.9 As expected, vibronic featureless absorption spectra gradually become slightly more structured and the asymmetry between absorption and fluorescence is much less pronounced at lower temperature. The temperature-dependent optical behaviors of OFs are similar to the observed behaviors in (unsubstituted) poly(p-phenylenevinylene) oligomers.54-56 The lack of symmetry between absorption and fluorescence is typical for π-conjugated hydrocarbons with low energetic torsional vibrational modes around C-C single bonds47,54 and has been ascribed to the enlarged torsional mobility of the molecules in the electronic ground state (S0) as compared to the first excited

J. Phys. Chem. B, Vol. 110, No. 20, 2006 9913

Figure 6. Vibrationally resolved absorption and emission spectra of R-(FL)2 and R-(FL)(FLO) at different temperatures. The experimental spectra of PF9 and a FL dimer31 in chloroform solution are shown for comparison.

state (S1).47,54 In OFs, the corresponding C2-C3 fundamental torsional mode has a frequency of only a few decades of wavenumbers in the gas phase, so that the average geometrical structure of oligofluorenes is nonplanar at room temperature. Besides, due to thermal excitation of vibrational modes, the higher vibrational energy levels are populated at higher temperature and the S0-S1 absorption spectrum may be generated from many superimposed torsionally excited initial states giving rise to broad subbands. Figure 6 also shows vibronic structures in the optical spectra of R-(FL)(FLO) at different temperature. As compared with R-(FL)2, the emission spectral profiles of R-(FL)(FLO) change drastically. After one of the FL units is replaced by a FLO unit, the emission maxima shifts toward lower energy and a dramatic decrease of blue PL intensity is observed. The emission maxima locates at 2.90 eV in R-(FL)2 while it locates at 2.43 eV in R-(FL)(FLO) at T ) 110 K. Our calculations further support the experimental measurements that the emission from PFs originated from two different species: excitations on pure chains and excitations that recombine at FLO defects.15-17,57 Recombination results in blue emission on pure chains while recombination at the FLO defect chains leads to a low-energy band in the emission spectra. R-(FL)2 exhibits much larger 0-0 energy gaps than (LPPP)2 and β-(FL)2. It can be explained by the fact that a large structural change occurs in the R-phase PF chain upon photoexcitation. The 0-0 energy gaps in R-(FL)2 are 0.34 eV at T ) 110 K and 0.36 eV at T ) 300 K, which agree with the experimental measurements.14-17,31 The 0-0 energy gaps of R-(FL)(FLO) are even larger than these of R-(FL)2. This fact demonstrates not only that large structural distortions occur in the excited state of R-(FL)(FLO) but also that the excitation energy is transferred from FL units to low-energy FLO sites since the efficient energy transfer to emissive chemical defects on the polymer chain can lead to a further substantial red shift of the apparent emissive species.58 4. Conclusions We have systematically presented theoretical investigations on the optical absorption and fluorescence spectra of semicon-

9914 J. Phys. Chem. B, Vol. 110, No. 20, 2006 ducting PFs to understand their structure-property relationships. The impacts of the chain morphology, oligomer length, chemical substitutent, and temperature on the nature of photoexcitations have been checked. Both the vertical absorption and vibrationally resolved optical absorption and fluorescence spectra have been calculated. Our work shows that a one-dimensional model for semiconducting PFs suffices to explain all the experimental data. The following conclusions have been achieved: (1) The chain morphological effects on the vertical absorptions of OFs are not significant. Three types of OFs have similar absorption spectral profiles. The discrepancy among the spectra is that β-(FL)n and (LPPP)n have lower vertical excitation energies and higher polarizabilities than R-(FL)n. The β-phase PFs thus have more extended conjugation length than R-phase PFs. (2) The optical properties of PFs have been predicted by the finite-size calculations. The singlet transition energies decrease with increasing oligomer length and converge for the longer oligomers toward a limiting value. The converged optical gaps are 3.11, 2.92, and 2.82 eV for R-phase and β-phase PFs and LPPP, respectively. (3) The vibronic structures with absorption and emission spectra are appreciably morphology-dependent. The absorption bands of β-(FL)n and LPPP oligomers exhibit a well-pronounced vibronic structure associated with high-energy, in-plane CdC stretch modes, similar to that observed in emission. But pure and FLO defect R-phase oligomers show a featureless absorption band and relatively well resolved emission spectra at ambient temperature. By fully taking into account the strongly anharmonic torsion potentials for the FL/FLO unit liberations around the long molecular axis, we have reproduced the experimentally observed absorption and emission features. The planarized β-(FL)n and LPPP oligomer show negligible 0-0 energy gaps whereas R-(FL)n and R-(FL)(FLO) have a wider 0-0 energy gap open. (4) The optical properties of PFs are temperature-dependent. As the temperature increases, the 0-0 energy gaps increase, the relative peak intensities redistribute, thermal broadening of the backbone mode VP appreciably increases, and the asymmetry of the absorption and fluorescence spectra in R-phase oligomers is significantly more pronounced. (5) Chemical substitutents have appreciable influence on both absorption and emission spectra of PFs. PFs are blue emitters that can act as efficient energy donors when coupled with appropriate energy acceptors, such as FLO. The energy acceptor species are dominantly emissive species and thus alter the PL emissions of pristine PFs. Contrary to the effect of one-chain FLO defects, MPA end cappers act as electron donors, which effectively balance the hole and electron currents in the polymer matrix and can thus improve the device efficiency of FL-based materials. Acknowledgment. Financial support from the National Science Foundation of China (No. 20333020, No. 20473080, and No. 50121202), a 973 project funded by National Basic Research Program of China (No. 2004CB719901), and the Chinese Academy of Sciences is acknowledged. All calculations are finished in the High Performance Computing Center of USTC. Supporting Information Available: The optical absorption spectra of a series of OFs, the schematic representation of MOs of OFs with and without chemical substitutents, and the optimal geometries of S0 and S1 states for FL dimers and trimers. This

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