Interplay of structural dynamics and electronic effects in an engineered assembly of pentacene in a metal–organic framework

Charge carrier mobility is an important figure of merit to evaluate organic semiconductor (OSC) materials. In aggregated OSCs, this quantity is determined by inter-chromophoric electronic and vibrational coupling. These key parameters sensitively depend on structural properties, including the density of defects. We have employed a new type of crystalline assembly strategy to engineer the arrangement of the OSC pentacene in a structure not realized as crystals to date. Our approach is based on metal–organic frameworks (MOFs), in which suitably substituted pentacenes act as ditopic linkers and assemble into highly ordered π-stacks with long-range order. Layer-by-layer fabrication of the MOF yields arrays of electronically coupled pentacene chains, running parallel to the substrate surface. Detailed photophysical studies reveal strong, anisotropic inter-pentacene electronic coupling, leading to efficient charge delocalization. Despite a high degree of structural order and pronounced dispersion of the 1D-bands for the static arrangement, our experimental results demonstrate hopping-like charge transport with an activation energy of 64 meV dominating the band transport over a wide range of temperatures. A thorough combined quantum mechanical and molecular dynamics investigation identifies frustrated localized rotations of the pentacene cores as the reason for the breakdown of band transport and paves the way for a crystal engineering strategy of molecular OSCs that independently varies the arrangement of the molecular cores and their vibrational degrees of freedom.

Pentacene assembled into 1D arrays using a metal–organic framework (MOF) approach. This cofacial packing motif, which is not present in pentacene bulk, shows an interesting interplay of band-like and hopping-type transport.     

Influence of lattice dynamics on charge transport in the dianthra[2,3-b:2',3'-f]-thieno[3,2-b]thiophene organic crystals from a theoretical study

The influence of lattice dynamics on carrier mobility has received much attention in organic crystalline semiconductors, because the molecular components are held together by weak interactions and the transfer integrals between neighboring molecular orbitals are extremely sensitive to small nuclear displacements. Recently, it has been shown that the dynamic disorder has little effect on hole mobility in the ab plane of pentacene, but a reasonable explanation is absent for such a puzzle. To better understand the effect of lattice vibrations on carrier transport, a further study is required for other organic materials. In this work, a mixed molecular dynamic and quantum-chemical methodology is used to assess the effect of nuclear dynamics on hole mobility in the dianthra[2,3-b:2',3'-f]-thieno[3,2-b]thiophene (DATT) crystals which exhibit high air stability with the hole mobility as large as that in rubrene-based devices. It is found that the lattice vibrations lead to an increasing encumbrance for hole transport in the ab plane of the DATT crystals as the temperature increases. By comparing the crystal structures of DATT and pentacene, the reduced hole mobility in DATT is attributed to the unsymmetric arrays of nearest-neighboring molecular dimers in the ab plane, because the electronic coupling exhibits unbalanced thermal fluctuations for the nearest-neighboring dimers which then induces a stronger oscillation for carriers along the directions with asymmetric packing. To further relate the dynamic disorder with hole transport, the variations of anisotropic mobilities are also analyzed. As a result, the negligible effect of lattice dynamics on the hole mobility in pentacene is explained by the centrosymmetric molecular packing of the nearest-neighboring molecular pairs in the ab plane.     

Effect of electronic polarization on charge-transport parameters in molecular organic semiconductors

Theoretical investigations of charge transport in organic materials are generally based on the "energy splitting in dimer" method and routinely assume that the transport parameters (site energies and transfer integrals) determined from monomer and dimer calculations can be reliably used to describe extended systems. Here, we demonstrate that this transferability can fail even in molecular crystals with weak van der Waals intermolecular interactions, due to the substantial (but often ignored) impact of polarization effects, particularly on the site energies. We show that the neglect of electronic polarization leads to qualitatively incorrect values and trends for the transfer integrals computed with the energy splitting method, even in simple prototypes such as ethylene or pentacene dimers. The polarization effect in these systems is largely electrostatic in nature and can change dramatically upon transition from a dimer to an extended system. For example, the difference in site energy for a prototypical "face-to-edge" one-dimensional stack of pentacene molecules is calculated to be 30% greater than that in the "face-to-edge" dimer, whereas the site energy difference in the pentacene crystal is vanishingly small. Importantly, when computed directly in the framework of localized monomer orbitals, the transfer integral values for dimer and extended systems are very similar.     

The nature of singlet excitons in oligoacene molecular crystals

A theory for polarized absorption in crystalline oligoacenes is presented, which includes Frenkel exciton coupling, the coupling between Frenkel and charge-transfer (CT) excitons, and the coupling of all neutral and ionic excited states to the dominant ring-breathing vibrational mode. For tetracene, spectra calculated using all Frenkel couplings among the five lowest energy molecular singlet states predict a Davydov splitting (DS) of the lowest energy (0-0) vibronic band of only -32 cm(-1), far smaller than the measured value of 631 cm(-1) and of the wrong sign-a negative sign indicating that the polarizations of the lower and upper Davydov components are reversed from experiment. Inclusion of Frenkel-CT coupling dramatically improves the agreement with experiment, yielding a 0-0 DS of 601 cm(-1) and a nearly quantitative reproduction of the relative spectral intensities of the 0-n vibronic components. Our analysis also shows that CT mixing increases with the size of the oligoacenes. We discuss the implications of these results on exciton dissociation and transport.     

Resonantly enhanced multiphoton ionization and zero kinetic energy photoelectron spectroscopy of chrysene: a comparison with tetracene

We report the electronic and vibrational spectroscopy of chrysene using resonantly enhanced multiphoton ionization (REMPI) and zero kinetic energy (ZEKE) photoelectron spectroscopy. As an isomer of tetracene, chrysene contains a kink in the middle of the four fused hexagonal rings, which complicates not just the symmetry but, more importantly, the molecular orbitals and hence vibronic transitions. Incidentally, the two nearby electronically excited states of chrysene have the same symmetry, and vibronic coupling introduces no out-of-plane vibrational modes. As a result, the REMPI spectrum of chrysene contains essentially only in-plane ring deformation modes, similar to that of tetracene. However, density functional calculations using gaussian even after the inclusion of vibronic coupling can only duplicate the observed REMPI spectrum in a qualitative sense, and the agreement is considerably worse than our recent work on a few pericondensed polycyclic aromatic hydrocarbons and on tetracene. The ZEKE spectrum of chrysene via the origin band of the intermediate electronic state S(1), however, can be qualitatively reproduced by a straightforward Franck-Condon calculation. The ZEKE spectra from vibrationally excited states of the S(1), on the other hand, demonstrate some degree of mode selectivity: the overall intensity of the ZEKE spectrum can vary by an order of magnitude depending on the vibrational mode of the intermediate state. A scaling factor in the theoretical vibrational frequency for the cation is also needed to compare with the experimental result, unlike tetracene and pentacene.     

Theoretical comparative studies on transport properties of pentacene,pentathienoacene, and 6,13‐dichloropentacene

Pentacene derivative 6,13‐dichloropentacene (DCP) is one of the latest additions to the family of organic semiconductors with a great potential for use in transistors. We carry out a detailed theoretical calculation for DCP, with systematical comparison to pentacene, pentathienoacene (PTA, the thiophene equivalent of pentacene), to gain insights in the theoretical design of organic transport materials. The charge transport parameters and carrier mobilities are investigated from the first‐principles calculations, based on the widely used Marcus electron transfer theory and quantum nuclear tunneling model, coupled with random walk simulation. Molecular structure and the crystal packing type are essential to understand the differences in their transport behaviors. With the effect of molecule modification, significant one‐dimensional π‐stacks are found within the molecular layer in PTA and DCP crystals. The charge transport along the a‐axis plays a dominant role for the carrier mobilities in the DCP crystal due to the strong transfer integrals within the a‐axis. Pentacene shows a relatively large 3D mobility. This is attributed to the relatively uniform electronic couplings, which thus provides more transport pathways. PTA has a much smaller 3D mobility than pentacene and DCP for the obvious increase of the reorganization energy with the introduction of thiophene. It is found that PTA and DCP exhibit lower HOMO (highest occupied molecular orbital) levels and better environmental stability, indicating the potential applications in organic electronics. © 2015 Wiley Periodicals, Inc.     

Vibronic coupling in molecules and in solids

We utilize the experience gained in our previous studies on the "chemistry of vibronic coupling" in simple homonuclear and heteronuclear molecules to begin assembling theoretical guidelines for the construction of potentially superconducting solids exhibiting large electron-phonon coupling. For this purpose we analyze similarities between vibronic coupling in isolated molecules and in extended solids. In particular, we study vibronic coupling along the antisymmetric stretch coordinate (Q(as)) in linear symmetric AAA molecules, and along the optical phonon "pairing" mode coordinate (Q(opt)) in corresponding one-dimensional [A]( infinity ) chains built of equidistant A atoms. This is done for a broad range of chemical elements (A). The following similarities between vibronic coupling in molecules and phonon coupling in solids emerge from our calculations: 1) The HOMO/LUMO electronic energy gap in an AAA molecule increases along Q(as), and the highest occupied crystal orbital/lowest unoccupied crystal orbital gap in [A]( infinity ) chain increases along Q(opt). 2) The maximum vibronic instability is invariably obtained for a half-filled, singly occupied molecular orbital in AAA molecules, and for a corresponding half-filled band in [A]( infinity ) chains. 3) The vibronic stability of an AAA molecule increases with a decrease of the AA bond length, as does the vibronic stability of [A]( infinity ) chains (external pressure may lead to a reversal of a Peierls distortion). 4) The high degree of s-p mixing and ionic/covalent forbidden curve crossing dramatically enhance the vibronic instability of both AAA molecules and [A]( infinity ) chains. We also introduce one quantitative relationship: The parameter log(R) (where R is molar refractivity, a parameter used by Herzfeld to prescribe the conditions for the metallization of the elements) correlates with a parameter f(AA) (defined as twice the electronegativity of A, divided by the equilibrium AA bond length), used by two of us previously to describe vibronic coupling in AAA molecules for a broad range of elements (A=halogen, H, or an alkali metal). We hope to illustrate that key chemical aspects of vibronic coupling in simple molecules may thus be profitably transferred to corresponding materials in the solid state.     

Dispersive and other second-order terms in exciton—phonon coupling

Analysis of the second-order corrections to the energy of an excited molecular crystal shows that there is an additional coupling between excitons and phonons which may be comparable to the usual resonance coupling. The new term couples even when the resonance term is small or zero, but does not contribute to exciton band splitting.     

Zero-point fluctuations in naphthalene and their effect on charge transport parameters

We calculate the effect of vibronic coupling on the charge transport parameters in crystalline naphthalene, between 0 and 400 K. We find that nuclear fluctuations can cause large changes in both the energy of a charge on a molecule and on the electronic coupling between molecules. As a result, nuclear fluctuations cause wide distributions of both energies and couplings. We show that these distributions have a small temperature dependence and that, even at high temperatures, vibronic coupling is dominated by the effect of zero-point fluctuations. Because of the importance of zero-point fluctuations, we find that the distributions of energies and couplings have substantial width, even at 0 K. Furthermore, vibronic coupling with high energy modes may be significant, even though these modes are never thermally activated. Our results have implications for the temperature dependence of charge mobilities in organic semiconductors.     

Molecular vibrations of [n]oligoacenes (n=2-5 and 10) and phonon dispersion relations of polyacene

As model compounds for nanosize carbon clusters, the phonon dispersion curves of polyacene are constructed based on density functional theory calculations for [n]oligoacenes (n=2-5, 10, and 15). Complete vibrational assignments are given for the observed Fourier-transform infrared and Raman spectra of [n]oligoacenes (n=2-5). Raman intensity distributions by the 1064-nm excitation are well reproduced by the polarizability-approximation calculations for naphthalene and anthracene, whereas several bands of naphthacene and pentacene at 1700-1100 cm(-1) are calculated to be enhanced by the resonance Raman effect. It is found from vibronic calculations that the coupled a(g) modes between the Kekulé deformation and joint CC stretching give rise to the Raman enhancements of the Franck-Condon type, and that the b(3g) mode corresponding to the graphite G mode is enhanced by vibronic coupling between the (1)L(a)((1)B(1u)) and (1)B(b)((1)B(2u)) states. The phonon dispersion curves of polyacene provide a uniform foundation for understanding molecular vibrations of the oligoacenes in terms of the phase difference. The mode correlated with the defect-sensitive D mode of the bulk carbon networks is also found for the present one-dimensional system.     

Emission band shape probes of the mixed-valence excited state properties of polypyridyl-bridged bis-ruthenium(II) complexes

The absorption spectra and emission spectral band shapes of several polypyridine-ligand (PP) bridged bis-ruthenium(II) complexes imply that the Ru(II)/Ru(III) electronic coupling is weak in their lowest energy metal to ligand charge transfer (MLCT) excited states. Many of these PP-bridging ligands contain pyrazine moieties and the weak electronic coupling of the excited states contrasts to the strong electronic coupling inferred for the correlated mixed-valence ground states. Although the bimetallic complexes emit at significantly lower energy than their monometallic analogs, the vibronic contributions to their 77 K emission spectra are much stronger than expected based on comparison to the monometallic analogs (around twofold in some complexes) and this feature is characteristic of bimetallic complexes in which the mixed-valence excited states are electronically localized. The weaker excited state than ground state donor/acceptor electronic coupling in this class of complexes is attributed to PP-mediated super-exchange coupling in which the mediating orbital of the bridging ligand (PP-LUMO) is partly occupied in the MLCT excited states, but is unoccupied in the ground states; therefore, the vertical Ru(III)-PP⁻ (MLCT) energy is larger and the mixing coefficient smaller in these excited states than is found for Ru(II)-PP in the corresponding ground states.     

A multimode analysis of the gas-phase photoelectron spectra in oligoacenes

We present a multimode vibrational analysis of the gas-phase ultraviolet photoelectron spectra of the first ionization in anthracene, tetracene, and pentacene, using electron-vibration constants computed at the density functional theory level. The first ionization of each molecule exhibits a high-frequency vibronic structure; it is shown that this regularly spaced feature is actually the consequence of the collective action of several vibrational modes rather than the result of the interaction with a single mode. We interpret this feature in terms of the missing mode effect. We also discuss the vibronic coupling constants and relaxation energies obtained from the fit of the photoelectron spectra with the linear vibronic model.     

“Proximity effects” in radiative transitions: a model study of the role of vibronic coupling and static crystal field interactions

We report the results of a model study of the influence of vibronic coupling involving non-totally symmetric vibrations and static crystal field interactions on the spectral properties of molecules with close-lying excited electronic states. The presented results suggests that “proximity effects” brought about by solvent perturbation arise from two sources: (i) alterations in the energy separation between vibronically coupled electronic states and (ii) crystal field mixing of the isolated molecular electronic states. It is shown that crystal field mixing leads to the breakdown of the vibronic coupling scheme for non-totally symmetric vibrations in isolated molecules. This breakdown is shown to have a very pronounced effect on the spectral properties of molecules with close-lying excited electronic states. The effect of environmental perturbations on excited state frequencies, the breakdown of symmetry and polarization selection rules, and vibrational intensity distributions is discussed.     

Le Couplage Vibronique dans une Chaine Linéaire de Molecules Etudié par une Méthode Auto-Cohérente

We describe the correlation diagram of a linear crystal, in the traditional framework of the vibronic coupling. All lattice normal modes, except the symmetrical mode, are coupled to the excitation transfer. We therefore propose an iterative method, where every mode “sees” an effective coupling arising from the interaction of the other modes with the electronic excitation. This method is applied to a simple case (the pentamer) and the results are compared with the exact solution. In the weak coupling case this procedure gives the vibronic band structure and in the strong coupling case, the electronic band accompanied by vibrational excitations. These results show that the method employed represents an interpolation approach.     

Vibronic spectra of the perylene crystal

The theory of vibronic coupling in the perylene-type molecular crystals containing four molecules in a unit cell is presented. The vibronic absorption spectra computed theoretically for the perylene crystal are in good agreement with the experimental ones in both the frequency and intensity distributions of two different crystal polarizations.     

Analysis of the vibronic fine structure in circularly polarized emission spectra from chiral molecular aggregates

Using a Frenkel-exciton model, the degree of circular polarization of the luminescence (g(lum)) from one-dimensional, helical aggregates of chromophoric molecules is investigated theoretically. The coupling between the electronic excitation and a local, intramolecular vibrational mode is taken into account. Analytical expressions for the fluorescence band shape and g(lum) are presented for the case of strong and weak electronic coupling between the chromophoric units. Results are compared to those from numerical calculations obtained using the three particle approximation. g(lum) for the 0-0 vibronic band is found to be independent of the relative strength of electronic coupling between chromophores and excitation-vibration coupling. It depends solely on the number of coherently coupled molecules. In contrast, for the higher vibronic transitions[g(lum)] decreases with decreasing strength of the electronic coupling. In the limit of strong electronic coupling, [g(lum)] is almost constant throughout the series of vibronic transitions but for weak coupling [g(lum)] becomes vanishingly small for all vibronic transitions except for the 0-0 transition. The results are interpreted in terms of dynamic localization of the excitation during the zero point vibrational motion in the excited state of the aggregate. It is concluded that circular polarization measurements provide an independent way to determine the coherence size and bandwidth of the lowest exciton state for chiral aggregates.     

Ultraviolet-visible-near infrared and mid-Fourier transform infrared spectroscopic studies of intermolecular interaction in cholesteryl oleyl carbonate in mesophases

Ultraviolet-visible-near infrared (UV-Vis-NIR) and Fourier transform infrared (FTIR) spectroscopic studies are presented of molecular association between like molecules of cholesteryl oleyl carbonate, each containing suitable pi-donor (steroid ring C=C) and pi-acceptor (C-O single bonds united with a C=O bond to give a carbonate group) moieties. Frequency shifts and intensity enhancements of donor and acceptor oscillators appear to be governed by reduced mass, vibronic coupling constants, and a few other parameters such as relative change in force constants, etc. Donor-acceptor complex formation is characterized not only by the appearance of new bands in the mid-FTIR spectrum but also by the emergence of a new, intense electronic band centered at approximately 3700 cm(-1), the so-called charge-transfer band, in the UV-Vis-NIR spectrum. This band is strong in the smectic-A and solid phases, but progressively diminishes when temperature is raised to realize the upper end of the cholesteric phase and eventually the isotropic phase. Also, a new, small electronic band at approximately 360 nm, only seen in the entire thermal range of the cholesteric phase, is attributed to the Lifshitz-van der Waals interaction between pretransitional smectic-A domains existing in the cholesteric phase. It is argued that mesophases may owe their thermodynamic stability to both Lifshitz-van der Waals and vibronic coupling (or electron-phonon coupling in extended systems such as smectics and solids) interactions.     

Crystal engineering for pi-pi stacking via interaction between electron-rich and electron-deficient heteroaromatics

New dipolar compounds containing alternating electron-rich thieno[3,2-b]thiophene units and electron deficient units have been synthesized. Compounds with 5-pyrimidinyl (compound 2) or benzothiazole (compound 5) as the electron-deficient unit were structurally characterized by the single-crystal X-ray diffraction method. The arrangement of the molecules is found to be one-dimensional slipped-pi-stack for 2. That of 5 is of slipped-pi-stack, albeit with a tilt angle between neighboring pi-stacks. The pi-pi interfacial distances of the molecules in the crystal lattice are 3.47 and 3.59 A for 2 and 5, respectively. On the basis of the crystal structure, compound 2, with negligible pi-pi slip along the short axis of the molecules, has a calculated electronic coupling value (0.153 eV) twice as large as that of the largest coupling of pentacene. Accordingly, the theoretically estimated hole mobility (mu(+)) for 2 (2.32 cm(2) s(-1) V(-1)) compares favorably with that of pentacene (1.93-5.43 cm(2) s(-1) V(-1)), despite of the larger reorganization energy for hole transport in 2. The symmetric intrastack S...C contacts found between the thieno[3,2-b]thiophene and pyrimidinyl units explain the unique features of the crystal structure of 2 and the resulting large electronic coupling.     

The high-pressure electronic structure of the [Ni(ptdt)2] organic molecular conductor

The electronic structure of the single component molecular crystal [Ni(ptdt)(2)] (ptdt = propylenedithiotetrathiafulvalenedithiolate) is determined at ambient and high pressure using density functional theory. The electronic structure of this crystal is found to be of the "crossing bands" type with respect to the dispersion of the HOMO and LUMO, resulting in a small, non-zero density of states at the Fermi energy at ambient pressure, indicating that this crystal is a "poor quality" metal, and is consistent with the crystal's resistivity exhibiting a semiconductor-like temperature dependence. The ambient pressure band structure is found to be predominantly one-dimensional, reflecting enhanced intermolecular interactions along the [100] stacking direction. Our calculations indicate that the band structure becomes two-dimensional at high pressures and reveals the role of shortened intermolecular contacts in this phenomenon. The integrity of the molecular structure is found to be maintained up to at least 22 GPa. The electronic structure is found to exhibit a crossing bands nature up to 22 GPa, where enhanced intermolecular interactions increase the Brillouin zone centre HOMO-LUMO gap from 0.05 eV at ambient pressure to 0.15 eV at 22 GPa; this enhanced HOMO-LUMO interaction ensures that enhancement of a metallic state in this crystal cannot be simply achieved through the application of pressure, but rather requires some rearrangement of the molecular packing. Enhanced HOMO-LUMO interactions result in a small density of states at the Fermi energy for the high pressure window 19.8-22 GPa, and our calculations show that there is no change in the nature of the electronic structure at the Fermi energy for these pressures. We correspondingly find no evidence of an electronic semiconducting-metal insulator transition for these pressures, contrary to recent experimental evidence [Cui et al., J. Am. Chem. Soc. 131, 6358 (2009)].