Theoretical calculation of the electro-absorption spectrum of the α-sexithiophene single crystal

Andrzejak, Marcin; Petelenz, Piotr; Slawik, Michał; Munn, R. W.

doi:10.1063/1.1484378

Cited by 37 publications

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“…Even though electro-optical modulation techniques have been also used to probe CTE's, a conclusive estimate of E B has not be given yet. 8,9 E DS , E B and E EPI depend on basic quantities such as intermolecular coupling, screening, and oscillator strength. A comparative analysis suggests that these quantities are similar in oligothiophenes, oligophenylenes, and oligophenylenevinylenes.…”

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Primary optical excitations and excited-state interaction energies in sexithiophene

et al. 2002

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Based on a unique combination of angle-resolved transmission spectroscopy and transmission data at high pressure, we identify the primary photoexcitations and the relevant excited-state interaction energies in a sexithiophene crystal. Optical excitations include charge-transfer excitons and Davydov polaritons. By extrapolation, we predict that in sexithiophene at hydrostatic pressures above 180 kbar, intermolecular excitations are lower in energy than intramolecular ones. The results are representative for a wide class of -conjugated molecular semiconductors because ͑1͒ the pertinent interaction energies and lengths scales are nearly identical and ͑2͒ published data on different molecules are consistent with our interpretation. DOI: 10.1103/PhysRevB.66.113102 PACS number͑s͒: 78.40.Me, 78.55.Kz, 78.66.Qn Linear -conjugated molecules, such as oligothiophenes, oligophenylenes, and oligophenylene-vinylenes, are attracting increasing attention for their use in electronic and optoelectronic devices.1 Despite the high technological interest, the knowledge of their fundamental electronic and optical properties remains inadequate for various aspects. Our interest is to address to the nature and interacting energies of the primary photoexcitations, for which long-lasting and unresolved controversies exist. [2][3][4][5][6] In the crystal, the lowest molecular excitation gives rise to as many intramolecular exciton bands as the number of nonequivalent molecules in the unit cell. The energy difference between the lowest and highest exciton transitions, the socalled Davydov splitting (E DS ), represents a fundamental energy scale, which provides an estimate of the intermolecular interaction strength in the excited state. Experimental optical spectra feature, however, complex patterns, which have precluded an unequivocal evaluation of E DS .In crystals, excitons with small wave vector k couple to photons with the same quasimomentum to yield a new particle called polariton. 7 The latter describes the photonexciton dynamics when the interaction energy (E EPI ) with photons exceeds any line broadening ͑strong-coupling regime͒. The polariton concept is the extension of the weakcoupling limit case, in which photons and delocalized excitations of matter are treated as independent particles. In linear -conjugated molecules, the lowest -* transition exhibits a very large oscillator strength (ӷ1). Therefore, we expect that polaritons, rather than bare excitons, are the primary photoexcitations in the crystal. The ensuing optical response can differ substantially from the one predicted in the weak-coupling regime.Besides intramolecular Frenkel excitons, crystals also support excitations for which the bound electron and hole reside on different molecules ͓charge-transfer excitons ͑CTE͔͒. The energy difference E B between these two kinds of excitations provides an estimate of the intermolecular interaction energy between electrons and holes. Positive ͑nega-tive͒ E B implies that stable exitations have an intramolecular ͑intermolecular...

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Primary optical excitations and excited-state interaction energies in sexithiophene

et al. 2002

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“…This new interpretational paradigm contrasted with the standard notion that Frenkel states give rise to first-derivative EA fingerprints, and was based on the ad hoc assumption [3] that for a strong electronic transition the transition dipole moment (i.e. an off-diagonal matrix element of the dipole moment operator) behaves much in the same way as the permanent dipole moment (a diagonal matrix element of the dipole moment operator).Specifically, this approach led to the conclusion that the EA spectrum of crystalline sexithiophene (T6) is dominated by Frenkel excitons [3], contrary to the results of quantitative calculations based on a microscopic Hamiltonian, which attributed a major part of the observed EA spectrum of T6 to chargetransfer states [6]. In the present paper, we probe the role of polariton effects by including them in the calculation of the EA spectrum of T6, with complete disregard of the CT manifold.…”

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“…Secondly, the calculated spectrum is much too weak (even in the unlikely case of all c*-polarized intensity being spilt into the b polarization), and its shape blatantly disagrees with the experimental spectrum, which shows that Frenkel transitions alone cannot explain the observed EA spectrum of sexithiophene. In contrast, the spectrum can be very well reproduced when CT states are properly included [6]; even the b-polarized component is then correctly accounted for without invoking any intensity spillage from the c*-polarization. This once again emphasizes the crucial role of charge transfer states for EA spectroscopy.…”

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confidence: 96%

“…We take into account only the lowest intramolecular excitation of the sexithiophene molecule, polarized along the long molecular axis, located at 2.50 eV, and endowed with the transition dipole moment of 2.1 eÅ [6]. The dipole sums for T6 were evaluated previously [10].…”

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confidence: 99%

“…In our present approach, the exciton characteristics are calculated from a quantum-mechanical Hamiltonian approach similar to that used previously in the calculations of the sexithiophene EA spectrum [6]. The main difference consists in ignoring the CT manifold.…”

Section: Model and Calculationsmentioning

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Microscopic calculation of polariton effects in molecular crystals – application to sexithiophene electroabsorption spectrum

Petelenz

Stradomska

2006

Phys. Status Solidi (c)

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An explicit formula expressing the refractive index in terms of exciton energies and oscillator strengths is used to calculate the absorption spectrum of the crystal at zero and non-zero electric field; the electroabsorption signal is calculated as their difference, without any a priori assumptions regarding the shape of the individual EA fingerprints. The approach is applied for the sexithiophene crystal. The results show that an isolated Frenkel exciton always yields a first-derivative EA signal, regardless of its intensity, and that this conclusion is not affected by polaritonic effects. For the specific case of sexithiophene, a satisfactory theoretical reproduction of the EA spectrum is possible only when the low-energy charge-transfer states are included.1 Introduction In the recent literature, there is considerable emphasis on the specific consequences of exciton-photon coupling for intense electronic transitions, which are rather common in the molecular systems of potential interest for optoelectronics, such as e.g. oligothiophenes [1][2][3].The features that are often associated with the formation of polaritons are: dependence of exciton energies on the direction of the k-vector (directional dispersion [4,5]) and the diffuse absorption shape, accompanied by the accumulation of intensity in the high-energy part of the exciton spectrum [1,4,5]; in the past several years there was also a claim [3] that owing to polariton effects, a Frenkel exciton could exhibit a second-derivative electro-absorption (EA) signal, normally attributed to charge-transfer (CT) states. This new interpretational paradigm contrasted with the standard notion that Frenkel states give rise to first-derivative EA fingerprints, and was based on the ad hoc assumption [3] that for a strong electronic transition the transition dipole moment (i.e. an off-diagonal matrix element of the dipole moment operator) behaves much in the same way as the permanent dipole moment (a diagonal matrix element of the dipole moment operator).Specifically, this approach led to the conclusion that the EA spectrum of crystalline sexithiophene (T6) is dominated by Frenkel excitons [3], contrary to the results of quantitative calculations based on a microscopic Hamiltonian, which attributed a major part of the observed EA spectrum of T6 to chargetransfer states [6]. In the present paper, we probe the role of polariton effects by including them in the calculation of the EA spectrum of T6, with complete disregard of the CT manifold. We are making no a priori assumptions regarding the shape of the polariton signal in electro-absorption; the obtained shape results from direct calculation. In this way, we test the hypothesis concerning the second-derivative EA fingerprint of exciton-polaritons, and directly reproduce their EA contribution for sexithiophene.

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Vibronic coupling in Frenkel and charge‐transfer states of oligothiophene crystals

Stradomska

Kulig

Petelenz

2010

Physica Status Solidi (b)

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Phone: þ48 12 633 22 12, Fax: þ48 12 634 05 15 A novel approach, recently proposed to describe excitonphonon coupling in Frenkel states of an infinite molecular crystal, is generalized to incorporate charge-transfer (CT) excitons. Both types of electronic excitations are treated on the same footing. The corresponding Hamiltonian in the LangFirsov representation is subdivided into subspaces representing one-particle, two-particle, etc., excitations, and (after truncating the basis set to manageable size) numerically diagonalized to yield the absorption as well as the electroabsorption (EA) spectrum. The emphasis is on the latter, previously reproduced only in the limiting cases of weak or strong vibronic coupling. The calculations are presented for the sexithiophene crystal, with parameterization based on independent experimental and theoretical estimates. 1 Introduction Viewed as a testing ground for theoretical description of excitons, the sexithiophene crystal (6T) offers a variety of challenges. One of them is a consequence of the fact that its spectroscopically dominant Frenkel excitons are coupled at the same time to intramolecular vibrations and to the manifold of charge-transfer (CT) states. Vibronic interaction in 6T qualifies as an intermediate-coupling case, which makes numerical calculations indispensable. The same applies to the CT interactions; combined, these two factors produce a numerical problem of large size and considerable complexity.To date, only partial attempts to solve it were undertaken. This was possible because the Frenkel and CT states have different realms of importance. While the Frenkel contributions are crucial for absorption/emission spectroscopy (where precise vibronic structure is very relevant), their manifestations in electroabsorption (EA) spectra are of lesser significance and relatively trivial to interpret; in contrast, the CT states dominate the EA signal (where the details of vibronic structure are less clearly marked), but in most cases only marginally contribute to absorption or emission. In effect, the different spectra were interpreted using complementary theoretical frameworks.

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Theoretical calculation of the electro-absorption spectrum of the α-sexithiophene single crystal

Cited by 37 publications

References 48 publications

Primary optical excitations and excited-state interaction energies in sexithiophene

Primary optical excitations and excited-state interaction energies in sexithiophene

Microscopic calculation of polariton effects in molecular crystals – application to sexithiophene electroabsorption spectrum

Vibronic coupling in Frenkel and charge‐transfer states of oligothiophene crystals

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