Article pubs.acs.org/JPCC
Exciton Binding Energy in Molecular Triads Stefan Kraner,*,†,‡ Giacomo Prampolini,¶ and Gianaurelio Cuniberti†,‡,§ †
Institute for Materials Science and Max Bergmann Center of Biomaterials, 01062 Dresden, Germany Dresden Center of Computational Materials Science, Technische Universität Dresden, D-01062 Dresden, Germany ¶ Istituto di Chimica dei Composti Organometallici (ICCOM-CNR), Area della Ricerca, I-56124 Pisa, Italy § Center for Advancing Electronics Dresden, Technische Universität Dresden, 01062 Dresden, Germany ‡
ABSTRACT: The power conversion efficiency of state of the art organic photovoltaics is predicted to be limited at about 15%. This limit can be increased by an improved charge carrier mobility and by a lower exciton binding energy. In order to achieve this, we suggest a concept based on organic triads, comprising a donor, spacer, and acceptor submolecule. On the basis of time dependent density functional theory (TD-DFT) simulations we investigate the lowest excited state of the wellknown Carotenoid-Porphyrin-C60 triad and obtain a calculated exciton binding energy of 25 meV, justifying the experimentally observed and reported separation of photo generated charges. Further, we introduce a new triad with the ability to not only improve and control the separation process, but also to improve the charge carrier transport properties. We used molecular dynamics (MD) simulations to optimize the geometry of a cluster of 25 triads. From this organic cluster, we picked one triad with its four neighbors, again calculated the exciton binding energy of this structure and obtained 39 meV. We conclude that the exciton binding energy is stable for a variety of different basis set and functionals, and does not significantly change if one or a cluster of five triads is simulated. This stable behavior occurs, since changes in the wave functions do not significantly influence the exciton binding energy, as long the distance between the positive and negative charge remains the same. For photovoltaic applications and based on organic materials with a dielectric constant of about four, we suggest the use of spacer molecules larger than two nanometers.
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INTRODUCTION Organic photovoltaics (OPV) represents a promising technology for a renewable, nontoxic, and low cost energy supply. Currently, the record power conversion efficiency of this technology is 13.2%, while commercial available organic solar cells exhibit power conversion efficiencies of about 8%.1,2 For large area applications the power conversion efficiency of OPV needs to be improved. However, it is expected that based on the currently used donor−acceptor system in OPV the achieveable power conversion efficiency is limited to about 15%.3 In organic solar cells, an absorbed photon creates a strongly bound exciton in the photoactive material. The exciton is then dissociated at the donor−acceptor interface, and the created charge carriers, i.e., the electron and the hole, can then move to their respective electrodes. The major loss in OPV is the voltage loss. The open circuit voltage is directly connected to the effective gap of the donor−acceptor blend.4 As shown in Figure 1, the donor−acceptor interface lowers the effective gap Egeff, and therefore also the achievable voltage of OPV, since the energy difference, also called LUMO−LUMO offset, between the optical gap Eopt of the donor and Egeff is needed for the dissociation of the photogenerated charges. In organic solar cells the LUMO−LUMO offset is in the range of 0.3−1 eV.3 It © XXXX American Chemical Society
Figure 1. Energy levels of the donor−acceptor blend. Egeff represents the effective gap of the donor−acceptor system, Eopt the optical gap of the donor material, the ionization potential (IP) of the donor, and the electron affinity (EA) of the acceptor material.
has been predicted that by lowering the LUMO−LUMO offset to 0.2 eV and by increasing the charge carrier mobility to at least 10−2 cm2/(V s), power conversion effieciencies above 20% are feasible.5 The low charge carrier mobilities in currently used Received: April 26, 2017 Revised: June 19, 2017
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DOI: 10.1021/acs.jpcc.7b03923 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
Figure 2. Molecular structure of the triads investigated, with the three submolecules: i.e. the donor (red bracket) on the left-hand side, the spacer (blue bracket) in the middle, and the acceptor (black bracket) on the right-hand side. Key: (a) Carotenoid-Porphyrin-C60; (b) OTTV-TTDA5TFBDOPV.
shown in Figure 2b, this triad consists of three submolecules, i.e., a thienothiadiazole-based oligomer (OTTV),15 a five membered oligothiophene (5T), whose central unit is substituted by a heterocyclicthieno[3,4-c][1,2,5]thiadiazole (TTDA5T),16 and the difluoro-benzo-difurandione-based tris(p-phenylenevinylene) (FBDOPV).17 The new triad is not only able to dissociate the charges but also provides potentially an improved charge transport for holes and electrons along the donor and acceptor phase, respectively. We use molecular dynamics (MD), carried out with accurate and specifically parametrized force-fields (FFs), to predict a possible arrangement of triads in a solid, and quantify the exciton binding energy of a small cluster of triads. It is shown that the investigated triads exhibit an intramolecular CT exciton binding energy in the range of the thermal energy, which in a solid leads to free moving charges, contributing to a useable photocurrent. In this framework, the present study may serve as a proof of concept to show that arranged triads can circumvent the two major problems in OPV, i.e., the voltage losses and the low charge carrier mobility.
donor−acceptor bulk heterojunction systems is the second major cause of efficiency loss. Indeed, the charge carrier mobilities in state of art organic solar cells are in the range of 10−5−10−3 cm2/(V s).6,7 In order to maximize the power conversion efficiency of an organic solar cell, low charge carrier mobilities usually led to a trade off between high absorption (by a thicker absorber layer) and recombination of photogenerated charges (due to the longer transport path).6 Higher charge carrier mobilities in the range of 0.1−6 cm2/(V s) can be achieved by a higher crystallinity of the organic molecules involved.8,9 Therefore, in order to significantly increase the power conversion efficiency in organic photovoltaics, the charge carrier mobility must be increased at least 1 order of magnitude, while the LUMO−LUMO offset must be reduced to at least 0.2 eV. Reducing the LUMO−LUMO offset can be accomplished by lowering the exciton binding energy of an intermolecular charge transfer (CT) state between the donor and acceptor molecule, which in turn can be achieved by increasing the dielectric constant at the interface, e.g. by using polar side-chains.10 In order to tailor the interface between the donor and the acceptor moiety, a defined spatial order is beneficial, which could be achieved by covalently bonded donor and acceptor molecules. However, it is known that the binding energy of an intermolecular CT state is still about one order of magnitue too high for thermal dissociation.10 It has been reported that the insertion of a spacer molecule in between the donor−acceptor pair composing a dyad (thus forming a triad system) increases the lifetime of the CT state by a factor of 10.11 Further, it is well-known that triads comprising a donor, spacer, and acceptor molecule can dissociate photogenerated charges.12,13 It has been reported, that a Carotenoid-Porphyrin-C60 triad, dependent on its conformation, exhibit a long-range charge separation state.14 Broadly speaking, the advantage of triads is the spatially defined donor− acceptor interface, which can be tailored in order to lower the voltage losses. Here, we use the TD-DFT method to calculate the exciton binding energy of the lowest lying CT state between the donor and acceptor molecule of two different triads. First, we investigate the exciton binding energy of the well-known and experimentally investigated Carotenoid-Porphyrin-C60 triad in solution (the structure is shown in Figure 2a). Then, we propose a new triad, optimized for photovoltaic purposes. As
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COMPUTATIONAL DETAILS QM Calculations and MD Simulations. All quantum mechanical (QM) calculations, carried out exploiting the density functional theory (DFT) or its time-dependent extension (TD-DFT), were performed with the Gaussian09 suite of programs.18 Unless differently stated, the QM calculations on single molecules were performed using the hybrid B3LYP functional with the 6-31G(d,p) polarized basis set. Geometry optimizations were carried out optimizing all coordinates without any restraint, whereas in torsional profiles only the scanned internal coordinate (IC) was constrained and the curves sampled stepwise every 30°. For molecular arrangements with several triads, geometry optimization by DFT is too time-consuming. Therefore, in order to obtain structures with several stacked OTTVTTDA5T-FBDOPV triads we use MD simulations for the geometry optimization. All classical molecular mechanics (MM) optimizations and MD simulations were performed by the Gromacs5.1.2 software.19 As far as the former are concerned, a molecular cluster made up of 25 triads was initially built through the B
DOI: 10.1021/acs.jpcc.7b03923 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
sample the IPES reliably, the interaction energies of several (>100) dimers was computed. At QM level, the CAM-B3LYP functional was employed, using the 6-31G* basis set and the empirical Grimme correction (GD323) to take dispersion into account. To handle the basis set superposition error (BSSE), the standard Counterpoise correction was applied in all cases.24 As previously done for the intramolecular term, the parametrization was carried out separately for each moiety (donor, spacer, and acceptor). For each building block, the final standard deviation was smaller than 1 kJ/mol. The parametrized FFs were validated by running several preliminary tests. First, the resulting MM normal modes were compared to the ones obtained by DFT calculation. The resulting comparison is shown for each submolecule in Figure 4, where a very good agreement between the QM and Joyce descriptions appears in describing the model harmonic vibrational behavior. Conversely, as far as more flexible and large amplitude motions are concerned, the rotation around single bonds of the dihedral evidenced in Figure 3 (D1−D12) was investigated in detail. For this comparison, again, we compare the energies obtained from DFT calculations with the values calculated based on the fitted FF. We not only evaluated the energies obtained from the JOYCE program, but also calculated the energies directly by MM optimizations. These fitted energies at varying dihedral angles exhibit a good agreement as compared to the values obtained by DFT calculations (see Figure 5). We further test the intramolecular FF by comparing the first excited state of the geometry optimized by MD simulation or by DFT calculations, whereas the starting geometry prior the optimization step is the same. On the basis of the used functional CAM-B3LYP and basis set 6-31g(d,p) we obtain an excitation energy of 1.509 eV and an oscillator strength of 2.226 for the geometry optimized by DFT calculations, whereas the geometry obtained by MD optimization gives an excited state energy of 1.510 eV with a oscillator strength of 2.239, indicating a good agreement between the two molecular geometries obtained. Exciton Binding Energies and Related Energy Levels. Reported frontier orbital energies have been calculated by tuned range separated hybrid functionals LC-ωB97XD with the basis set 6-31G(d,p). Tuned range separated functionals have been reported to provide energies in a good agreement to experimental values.25,26 In this approach the parameter ω is tuned to an optimized value such that exact exchange exhibits the correct asymptotic behavior, in order to cancel the asymptotic self-interaction.27 This is achieved when the negative IP equals the energy of the HOMO εHOMO, and the negative EA equals the energy of the LUMO εLUMO, whereas the IP is calculated by the total energy (self-consistent field)
Avogadro Software (http://avogadro.opnemolecules.net), and then optimized at MM level using the Gromacs package. To this end, the steepest descent minimization algorithm was employed, in double precision format, using the convergence criterion of a maximum present force to be below 100 kJ/mol/ nm. All MM and MD calculations were performed making use of accurate FFs, specifically parametrized as described in some detail in the following. FF Parametrization. The FF parametrization was carried out separately for the intra- and intermolecular terms, exploiting the Joyce and Picky20−22 softwares, respectively. These tools allow to parametrize organic molecules on the basis of QM calculations. To reduce the computational burden, we divided the triad used for MD investigation, i.e., OTTVTTDA5T-FBDOPV, into three subparts, the OTTV, the TTDA5T, and the FBDOPV molecule. The molecular structures of the investigated triads are shown in Figure 3,
Figure 3. Molecular structure of the triad investigated by MD simulations (cyan = carbon, yellow = sulfur, blue = nitrogen, red = oxygen, magenta = fluorine, and white = hydrogen). D1−D12 represent the calculated flexible dihedrals considered in FF parametrization and MD simulations. The brackets evidence the molecular building blocks employed in the FF parametrization: from left to right, red, blue, and black brackets indicate donor, spacer, and acceptor moieties, respectively.
where the different moieties constituting the triads (i.e., donor, spacer or acceptor) are evidenced in different colors. For each moiety, the parameters of the intramolecular terms were obtained by means of the Joyce software, based on geometries, energies and ground-state Hessian matrices purposely computed at QM level (B3LYP/6-31G(d,p)). The Joyce standard protocol was followed, minimizing the least squared difference between MM and stored QM data. Turning to the intermolecular part, the FF parameters governing the interaction among different molecules (i.e., Lennard-Jones and point charges) were obtained through the Picky software. The standard Picky procedure was employed, based on a nonlinear fitting of the least-squares differences between the interaction potential energy surface (IPES) computed at QM level and the one obtained at MM level with the Picky FF. To
Figure 4. Normal modes calculated by DFT and by to FF obtained from the JOYCE software for the three submolecules OTTV, TTDA5T, and FBDOPV. C
DOI: 10.1021/acs.jpcc.7b03923 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
Figure 5. Energies obtained for molecules with different dihedral angles. Energies have been obtained by DFT and MD simulations. The data calculated from MD simulations have been calculated by the JOYCE software or by the Gromacs program.
difference between to cation and the neutral molecule. Similarly, the EA is calculated by the difference between the anion and the neutral molecule. ω is chosen in order to minimize the least-squares failure J*(ω) calculated by eq 1.27
e2 EC = 4πε0εr
(εHOMO(ω) + IP(ω))2 + (εLUMO(ω) + EA(ω))2
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(1)
All optimized J* obtained have been below 0.038. Unless differently stated, TD-DFT calculations have been conducted on a CAM-B3LYP/6-31g(d,p) level of theory. For the calculations in thin films or solution polarization effects have been approximated by using the conductor like PCM model (CPCM).26 The dielectric constant of the solution for Carotenoid-Porphyrin-C60 is 7.6 (TetraHydroFuran), while for the calculations of the OTTV-TTDA5T-FBDOPV triad, we used the relative dielectric constant εr obtained by applying the Clausius Mossotti equation, which is valid for nonpolar materials and for amorphous or cubic structures: εr − 1 4π 1 = α′ 3 VM εr + 2
1
2
(3)
where e is the elementary charge, ε0 is the vacuum permittivity, and ρ represents the densities of the natural transition orbitals (NTOs) of the hole ρh and the particle (electron) ρe with their ⎯r and → ⎯r , respectively. The NTOs are derived by coordinates→ 1 2 the Cubgen tool included in the Gaussian 09 suite.
J *(ω) =
∫∫
⎯r )ρ (→ ⎯ ρh (→ 1 e r2) → ⎯r d3⎯r1 d3→ 2 → ⎯ → ⎯ |r − r |
RESULTS
The Exciton Binding Energy in Carotenoid-PorphyrinC60. As introduced, in order to optimize organic photovoltaics, it is beneficial to control the separation and the transport of the photogenerated charges. It is well-known that the triad Carotenoid-Porphyrin-C60 generates charge separated states, where the electron is located on the C60 and the hole on the carotenoid molecule. The measured lifetime of this CT state has been reported to be 340 ns.30 DFT calculations show that the charges in this CT state are about 50 Å separated from each other, making this triad interesting for photovoltaic applications. Here, we calculate the exciton binding energy of the lowest excited state of the triad in its linear configuration, whereas we used the geometry published in the Supporting Information of ref 14. The observed charge transfer for the electron to the C60 and the hole to the Carotenoid molecule is certainly driven by an energy gradient within the triad. We calculated the energies of the three conjugated submolecules. The submolecules are shown in Figure 3. The submolecules used for calculations have been complemented with hydrogen atoms at the linker positions, whereas a geometry optimization of the submolecules has been performed prior to the energy calculations. As shown in Figure 6, the IP of the three submolecules exhibit a ”cascade” behavior, indicating an efficient transport of the hole to the
(2)
with the molecular volume VM, and the polarizability volume α′. The molecular volume has been obtained from the optimized geometry of the molecular cluster of 25 OTTV-TTDA5TFBDOPV triads, whereas the polarizability volume has been calculated by DFT from a single triad (B3LYP/6-31G(d,p)). The exciton binding energy is the Coulomb attraction between the hole and the electron minus the kinetic energies of these quasi particles.28 We numerically calculate the Coulomb attraction EC by using eq 329 D
DOI: 10.1021/acs.jpcc.7b03923 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
separate and transport photogenerated charges, in the next section we investigated a triad based on three planar submolecules, which are potentially able to form π-stacks, which is known to be beneficial for an efficient charge transport. The Exciton Binding Energy in OTTV-TTDA5TFBDOPV. Using triads for charge separation and a beneficial order, e.g. a π-stacking of acceptor molecules on each other and donor molecules on each other, paves the way to increase the currently present power conversion efficiency limit. It has been shown that FBDOPV exhibits a charge carrier mobility for electrons as high as 1 cm2/(V s),17,32 while holes can be transported efficiently by thiophene based molecules.33 The spacer molecule should exhibit energy levels between the EAs and IPs of the donor and acceptor molecule, building up a molecular energy cascade. As shown in Figure 8, we obtain
Figure 6. EA and IP energies of the three submolecules from the Carotenoid-Porphyrin-C60 triad, whereas the three chemical structures reflect the isolated submolecules used for these DFT calculations.
Carotenoid molecule, while the EA has its lowest state in the Pyrrole-C60 moiety. This behavior has already been reported.31 On the basis of these calculations an electron created in the Carotenoid molecule must overcome a small barrier to finally reach the acceptor molecule, i.e., the Pyrrole-C60, which might explain the observed lower yield (
