Letter pubs.acs.org/JPCL
Cite This: J. Phys. Chem. Lett. 2017, 8, 5943−5948
Theory of Transient Excited State Absorptions in Pentacene and Derivatives: Triplet−Triplet Biexciton versus Free Triplets Souratosh Khan† and Sumit Mazumdar*,†,¶,§ †
Department of Physics, University of Arizona, Tucson, Arizona 85721, United States Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, United States § College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, United States ¶
S Supporting Information *
ABSTRACT: Recent experiments in several singlet-fission materials have found that the triplet−triplet biexciton either is the primary product of photoexcitation or has a much longer lifetime than believed until now. It thus becomes essential to determine the difference in the spectroscopic signatures of the bound triplet−triplet and free triplets to distinguish between them optically. We report calculations of excited state absorptions (ESAs) from the singlet and triplet excitons and from the triplet−triplet biexciton for a pentacene crystal with the herringbone structure and for nanocrystals of bis(triisopropylsilylethynyl) (TIPS)-pentacene. The triplet−triplet biexciton absorbs in both the visible and the near-infrared (NIR), while the monomer free triplet absorbs only in the visible. The intensity of the NIR absorption depends on the extent of intermolecular coupling, in agreement with observations in TIPS-pentacene nanocrystals. We predict additional weak ESA from the triplet−triplet but not from the triplet, at still lower energy. inglet fission (SF)1,2 in organic molecules refers to dissociation of the optical singlet exciton S1 of an organic molecule or conjugated polymer into the two lowest triplet excitons T1, according to the scheme
S
seconds.12 A similar conclusion has been reached for crystals and films of TIPS-tetracene.13,14 In other cases, the conclusion that the 1(TT)1 is the primary photoproduct was reached by performing transient measurements that could distinguish between the 1(TT)1 and T1. The latter is true for one family of bipentacenes11 as well as a donor−acceptor (DA) conjugated polymer.15 Importantly, in both of these latter cases, the same conclusion was arrived at independently from theoretical calculations of the 1(TT)1 and ESAs from this state.8,16 Both theoretical calculations and experimental transient absorption measurements found additional PAs from the 1(TT)1 that are absent in excitations from T1. Here we extend our theoretical investigation to two of the most well-studied systems, films and crystals of pentacene and nanocrystals of TIPS-pentacene. Early measurements on pentacene films claiming observation of free triplets T1 are not considered conclusive as the measurements were in the visible range of the electromagnetic spectrum, where singlet and triplet PAs are overlapping.17 Later transient absorption studies18 assigned a broad PA at ∼750−950 nm in the nearinfrared (NIR) to triplet PA T1 → T2. More recent experimental works on pentacene as well as TIPS-pentacene make the same assignment.19,20 This assignment of the NIR PA to T1 has, however, been questioned.5,6 Theoretical calculations of pentacene monomer within the Pariser−Parr−Pople (PPP) π-electron model21,22 with electron hopping between only
S0 + S1 → 1(TT)1 → T1 + T1
where S0 refers to the singlet ground state and 1(TT)1 is a correlated triplet−triplet bound biexciton.3−5 Here the superscript refers to singlet spin multiplicity and the subscript to the quantum number of the state. Experimental detection of SF is made by time-resolved spectroscopy; SF requires the paired decay of the singlet S1 → SN transient photoinduced absorption (PA) and the rise of long-lasting triplet T1 → TN PA (here SN and TN are higher singlet and triplet excitations, respectively). Confirmed identification of T1 as the primary product of photoexcitation therefore requires distinguishing between PA from the 1(TT)1 and T1. The precise nature of the 1(TT)1 wave function is still under discussion,6−10 while theoretical work on excited state absorptions (ESAs) from 1(TT) 1 is just beginning.8 The motivation of our theoretical work comes from multiple recent experimental studies that have indicated that in several likely candidates for SF the primary photoproduct is actually the bound 1(TT)1 and not T1, or the 1(TT)1 has a much longer lifetime than believed until now.11−15 In some cases, these conclusions were arrived at by performing additional experiments beyond measurements of transient absorption alone. Thus, on the basis of direct emission from the 1(TT)1 in films of pentacene and other acene derivatives, the lifetime of the 1 (TT)1 was estimated to range from 1 to 100s of nano© XXXX American Chemical Society
Received: October 16, 2017 Accepted: November 22, 2017 Published: November 22, 2017 5943
DOI: 10.1021/acs.jpclett.7b02748 J. Phys. Chem. Lett. 2017, 8, 5943−5948
Letter
The Journal of Physical Chemistry Letters
Figure 1. (a) Herringbone structure of pentacene. The lattice parameters were taken from refs 43 and 44. All calculations are for the dimer, indicated in the figure. (b) Calculated absorption spectra, superimposed on the experimental low-temperature absorption spectrum of pentacene film.18 (c) Dominant contributions to the normalized singlet excited states of the dimer in the pentacene unit cell, for U = 6.0 eV, κ = 1.8, and β = −0.2 eV. Only the frontier orbitals’ HOMO and HOMO−1 (red) and LUMO and LUMO+1 (blue) and their occupancies are shown. The bonds represent spin-singlet excitations. The double excitation indicated includes the total normalized contribution by all T1 ⊗ T1 configurations. The last column gives the overall CT contributions to the wave functions. The three excited states to which ground state absorption occurs are labeled S0S1 (a−c), respectively. (d) Calculated ESA spectrum from the lowest S0S1 in the IR. The inset shows the calculated singlet ESA for the monomer, where a single ESA occurs in the IR. Experimental observation of two PAs in the IR19,28 is a clear signature of strong CT contribution to S0S1.
nearest neighbors find zero oscillator strength for the triplet ESA in this region.6,23 Coupled cluster calculation that did not have the nearest-neighbor restriction found the oscillator strength to be nonzero but still 2 orders of magnitude smaller than the ESA in the visible.24 Experimental solution studies of pentacene25 and tetracene26 have found the oscillator strength of the T1 ESA in the NIR to be anywhere from vanishing to several hundred times smaller than that in the visible, in agreement with theory.6,23,24 Very recent measurement of TIPS-pentacene in solution has yielded results reminiscent of that in tetracene.27 It has also been claimed from experiments in solids of pentacene derivatives that the 1(TT)1 absorbs in the same NIR wavelength region.28,29 A consensus here requires complete theoretical understanding of the 1(TT)1 in pentacene and TIPS-pentacene films, as well as the origin of the PA in the NIR. Extended PPP Hamiltonian. 21,22 With the pentacene herringbone and TIPS-pentacene crystals in mind, we consider the extended PPP Hamiltonian HPPP = Hintra + Hinter
Hintra =
tijμ(cμ†̂ iσcμ̂ jσ + cμ†̂ jσcμ̂ iσ ) + U ∑ nμ̂ i ↑nμ̂ i ↓
∑ μ , ⟨ij⟩, σ
+
μ,i
∑
Vij(nμ̂ i − 1)(nμ̂ j − 1) (2)
μ,i
