- Email: [email protected]
Charge-transfer excitons of metal intercalated pentacene dimers
Chemical Physics Letters 729 (2019) 1–5
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
Charge-transfer excitons of metal intercalated pentacene dimers
T
Mufasila Mumthaz Muhammed, Aalyah Saqer Alotaibi, Fathima Alkhashman, ⁎ Junais Habeeb Mokkath Quantum Nanophotonics Simulations Lab, Kuwait College of Science And Technology, Doha Area, 7th Ring Road, P.O. Box 27235, Kuwait
H I GH L IG H T S
dynamics of technologically relevant organic systems is important for solar energy conversion. • Exciton TD-DFT, we investigate the exciton dynamics of both the pristine and zinc (Zn) intercalated pentacene dimers. • Using • Zn intercalation enhances the generation of low-energy charge-transfer excitons.
A B S T R A C T
The precise understanding of the exciton dynamics of technologically relevant organic systems is important for a plethora of applications, including solar energy conversion. Using state-of-the-art quantum chemical calculations based on time dependent density functional theory, we investigate the exciton dynamics of both the pristine and zinc (Zn) intercalated pentacene dimers as a function of the inter-molecular distances. We elucidate that the key difference in the exciton dynamics of pristine (Zn intercalated) pentacene dimers is that in the former (latter) the exciton size increases (decreases) with the increasing inter-molecule distances. Importantly, Zn intercalation causes increasing overlap between the electron and hole states and enhances the generation of low-energy charge-transfer excitons. We believe that our theoretical results are important for the emerging field of organic materials for solar-based applications.
1. Introduction An in-depth understanding on the exciton dynamics of organic semiconductors is imperative for improving the performance of organic solar cells [1–10] and light-emitting diodes [11,12], to list a few. It is well-known that the size and shape of the organic molecules strongly influences their exciton dynamics. Additionally, in the case of conjugated molecular systems, the exciton dynamics can be modified through stacking of the sub-units [13–16]. In a related context, it is reported that the charge-transfer state is energetically the lowest state of a conjugated molecular system. Consequentially, a higher lying excited state can efficiently relaxes to a charge-transfer state. In this context, state-of-the-art quantum chemical calculations have enhanced our understanding of organic molecules considerably by giving a firstprinciples description of the exciton dynamics [17–27]. In this paper, our goal is to elucidate the exciton dynamics of pristine and Zn intercalated pentacene (C22H14: five benzene rings joined in an armchair manner) dimers as a function of the inter-molecule distances. The choice of pentacene molecules is motivated by its rich exciton (coupled electron-hole pairs) physics [28]. Pentacene shows a strong Davydov splitting of the exciton spectra [29,30]. In
⁎
addition to being a classic organic semiconductor with high carrier mobility [31] pentacene is well-known for its propensity for singlet fission [32–34]. In this study, we show that Zn intercalation enables the emergence of charge-transfer excitons and their characteristics can be easily tuned by varying the inter-molecule distances. The paper is organized as follows. First, we describe the geometrical features of the investigated systems and the simulations methods employed. We show our results and discuss them in the next section, presenting a detailed analysis of the optical excitations and exciton dynamics. The conclusion and outlook section close the paper. 2. Computational aspects All calculations are performed with ORCA DFT/TD-DFT software (version 4.0) [35]. The geometry optimization of the single pentacene monomer was carried out using the b3-lyp exchange-correlation functional (non-local orbital exchange of 20%) [36] with dispersion corrections using Grimme’s DFT-D3 approach [37] and def2-TZVP basis set [38]. Further information regarding the DFT calculation parameters and/or the exchange correlation functional used is available in the ORCA manual. The SCF convergence was set to 10−8. A gradient
Corresponding author. E-mail address: [email protected] (J.H. Mokkath).
https://doi.org/10.1016/j.cplett.2019.05.017 Received 20 March 2019; Received in revised form 9 April 2019; Accepted 10 May 2019 Available online 13 May 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.
Chemical Physics Letters 729 (2019) 1–5
M.M. Muhammed, et al.
convergence criterion of 10−6 and an energy convergence criterion of 10−6 were used in order to obtain well-converged pentacene monomer geometries. The optical spectra were computed using TD-DFT technique [39] in frequency space using b3-lyp functional. The choice of this hybrid exchange correlation functional is motivated by the fact that pentacene is well known to have rich excitonic physics. We found 100 roots are needed to compute the absorption spectrum up to an energy of 5.0 eV. All absorption spectra are broadened by Gaussian smearing of width σ = 0.10 eV. We seek understanding on the nature of the dominant peaks in the optical absorption spectrum using the transition density plots (it is a generalization of the transition dipole moment describing the transition between the Nth excited state and ground state) since they allow easy visual inspection of the optical excitations. The exciton analysis were performed with the theoDORE software [40,41]. The essence of the technique is to construct and analyze a twoparticle exciton wavefunction, which is given in terms of the positions and of the electron and hole quasi-particles. Further information regarding the calculation parameters is available in the theoDORE manual. An approximate exciton size (computed as the root-meansquare electron-hole separation) is calculated by using the following equation,
dexc =
∑MN
2 ΩMN dMN . Ω
Table 1 Optical gaps and exciton sizes of pentacene monomer, pentacene dimers, and pentacene dimers intercalated with Zn for d = 3, 4, 5 and 6 Å. System Pentacene Pentacene Pentacene Pentacene Pentacene Pentacene Pentacene Pentacene Pentacene
monomer dimer (d = 3 dimer (Zn) (d dimer (d = 4 dimer (Zn) (d dimer (d = 5 dimer (Zn) (d dimer (d = 6 dimer (Zn) (d
Å) =3 Å) =4 Å) =5 Å) =6
Å) Å) Å) Å)
Optical gap (eV)
Exciton size (Å)
2.10 2.20 1.86 4.25 1.67 4.21 1.80 4.17 1.80
5.56 5.83 5.52 6.23 5.92 7.06 4.74 7.84 4.30
particle transitions. Further insights into the aforementioned excitations can be obtained from their corresponding transition density plots, see Fig. 1. By inspecting the transition density plots, one can easily confirm that the 2.10 eV (4.0 eV) excitation exhibits the electron delocalization along the transverse (longitudinal) direction of the pentacene monomer. Table 1 shows that the calculated optical gap of the pentacene monomer is 2.10 eV. This is in agreement with the previous theoretical [optical gap of 2.20 eV using G0W0(PBE)] results [42] and experimental [optical gap of 2.30 eV using UV–visible spectroscopy] [43] results. The calculated exciton size of the pentacene monomer is 5.56 Å, see Table 1. Having discussed the nature of the optical excitations and exciton dynamics of the pentacene monomer, now we draw attention on pentacene dimers having inter-molecule gap distances (d) vary in the range of 3 to 6 Å, see Fig. 2. It should be recalled that when two or more monomers come into contact, not only do coupling between the excited states on each monomer have to be taken into account, but also chargetransfer states come into play. For example, in a dimeric system there are four states per type of monomer transition: a local excitation on each monomer and two charge-transfer states going in either direction. For small d values, all four states may couple to each other, producing highly complex mixed states [44]. Naively, it can be expected that more highly complex coupled states would emerge due to the Zn intercalation since a large number of possible local and charge-transfer states come into play. In addition, it is important to emphasize that the structure variations produce a marginal effect on the absorption profile, see Fig. S1 in the supporting information. Therefore, we believe that our model
(1)
where M and N are two atom indices, dMN is the distance between them and ΩMN is the probability of charge transfer from M to N. 3. Results and discussion Before discussing the optical excitations and exciton dynamics of the pristine and Zn intercalated pentacene dimers, it is instructive first to analyze the optical characteristics of the basic building blocks, i.e. the pentacene monomer. To this aim, we plot in Fig. 1 the optical absorption spectrum of the pentacene monomer in the energy range of 0 to 5.0 eV. The spectrum is characterized by two peaks centered at 2.10 eV [consists of 2 single-particle transitions, composed of HOMO→ LUMO (97%) and HOMO−2→LUMO+3 (3%)] and 4.0 eV [consists of 4 single-particle transitions, mainly composed of HOMO−2→LUMO (40%) and HOMO→LUMO+3 (31%)]. Note that 2.10 eV excitation is almost fully contributed by HOMO-to-LUMO transition, characteristic of an exciton. However, 4.0 eV excitation is composed of several single-
Fig. 1. TDDFT calculated optical absorption spectrum of pentacene monomer. Transition density plots corresponding to the excitations are also shown in Figure. Red and green color denote electron density accumulation (depletion) regions during the excitation, respectively. Both densities are plotted using the same iso-surface contour value. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 2. TDDFT calculated optical absorption spectrum of pentacene dimers as a function of d in the range of 3 to 6 Å. Transition density plots corresponding to the excitations are also shown in Figure. Red and green color denote electron density accumulation (depletion) regions during the excitation, respectively. Both densities are plotted using the same iso-surface contour value. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
respect to the d = 3 Å of the pristine pentacene dimer shown in Fig. 2). In particular, the spectral intensity of the strong excitation located between 4.0 and 4.5 eV is significantly reduced. The transition density plots corresponding to the different excitations depicts a mixed excitation. Note that this type of scenario is completely different for d in the range of 4 to 6 Å. In the case of d = 4 Å, one records the appearance of a low-energy excitation centered at 1.70 eV. The transition density plot corresponding to this excitation [mainly composed of HOMO→ LUMO (95%)] yields a charge-transfer exciton. It is important to mention that the small spectral intensity of the charge-transfer exciton results from the small spatial overlap of orbitals localized on individual pentacene monomers. The transition density plot corresponding to the strong excitation centered at 4.05 eV [consists of 10 single-particle transitions, mainly composed of HOMO−2→LUMO (42%) and HOMO−3→LUMO+3 (20%)] yields a local exciton confined to the individual pentacene monomers. Upon increasing the d value to 5 and 6 Å, one clearly observes significant modifications in the low-energy charge-transfer exciton. In particular, the inner region of the transition density plot becomes more closer to the intercalated Zn atom. This feature is highly pronounced for d = 6 Å since the inner region of the transition density plot becomes very much closer to the intercalated Zn atom. This results could have major implications on the exciton sizes. Table 1 shows that Zn atom intercalation causes sizable reduction of the exciton sizes [4 Å (5.92 Å) ⟶ 5 Å (4.74 Å) ⟶ 6 Å (4.30 Å)]. This is due to the fact that Zn intecalation enhances the interaction of the electron states of the individual pentacene monomers and affects the dynamics of the charge-transfer excitons. It is important to emphasize that the formation of charge-transfer excitons has strong implications in the singlet fission process where a photo-induced singlet excited state down-converts to two triplets, resulting in long-lived excitons and potential solar conversion quantum efficiencies exceeding 100% [46]. The efficacy of singlet fission depends sensitively on the nature of chargetransfer excitations, in the sense that electron and hole reside on different molecules, can accelerate singlet fission.
systems (two pentacene molecules with parallel orientations) and calculations will be valid as far as their optical response is concerned. Let us begin our analysis starting from the smallest considered d value of 3 Å. Apparently, one finds three excitations centered at 2.20 eV, 3.20 eV, and 4.30 eV, see Fig. 2. Transition density plots corresponding to the excitations are also shown in the figure. The transition density plot corresponding to the 2.20 eV peak [consists of 4 singleparticle transitions, mainly composed of HOMO→LUMO+2 (44%) and HOMO−1→LUMO+1 (36%)] depicts a local exciton confined to the individual pentacene monomers, whilst the 3.20 eV peak [mainly composed of HOMO−2→LUMO+1 (86%)] depicts a charge-transfer exciton, and 4.30 eV peak [consists of 12 single-particle transitions, mainly composed of HOMO−1→LUMO+10 (20%) and HOMO−6→ LUMO+3 (20%)] depicts a mixed excitation having a local and chargetransfer excitation components. It is noteworthy that for d = 4, 5, and 6 Å, there appears only one (strong and focused) excitation (located in the energy range between 4.0 eV to 4.5 eV) in the absorption spectrum and the low-energy excitations (present in the case of d = 3 Å) are completely vanished from the absorption spectrum. Apparently, the aforementioned strong excitation slightly red-shifts with the increasing d value in the range of 3 to 6 Å. Transition density plots corresponding to these peaks depict a mixed excitation. Now let us analyze the differences in the exciton size of pristine pentacene dimers as a function of the d values, see Table 1. The first remarkable observation is a uniform exciton size scaling (i.e. the growth of exciton size with the d) [45]. Specifically, for d = 3, 4, 5, and 6 Å, the calculated exciton sizes are 5.83 Å, 6.23 Å, 7.06 Å, 7.84 Å, respectively. After discussing the influence of inter-molecule distances on the optical excitations and exciton dynamics of the pristine pentacene dimers, we now present a similar analysis on Zn intercalated (in the geometrically central position between the monomers) pentacene dimers, see Fig. 3. The calculated results are cross-compared with the results shown in Fig. 2. In the case of d = 3 Å, one concludes that the effect of Zn intercalation is to slightly red-shift the excitations (with 3
Chemical Physics Letters 729 (2019) 1–5
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Fig. 3. TDDFT calculated optical absorption spectrum of pentacene dimers intercalated with Zn atom as a function of d in the range of 3 to 6 Å. Transition density plots corresponding to the excitations are also shown in Figure. Red and green color denote electron density accumulation (depletion) regions during the excitation, respectively. Both densities are plotted using the same iso-surface contour value. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. TDDFT calculated optical absorption spectra of pentacene dimers intercalated with Zn atoms in the range of 1 to 5 (d fixed to 4 Å).
Fig. 5. TDDFT calculated optical absorption spectra of pentacene dimers intercalated with Ca atoms in the range of 1 to 5 (d fixed to 4 Å).
We have examined the impact of Zn concentration (in the range of 1 to 5 atoms) on the pentacene dimer absorption profile (see Fig. 4), finding systematic developments in the spectral evolution. In addition, we have also examined the impact of other atomic species on the spectra evolution. To this aim, we chose calcium (Ca) atoms (relevant in hybrid organic/inorganic applications). Apparently, Fig. 5 shows that the key effect of increasing the Ca concentration is to systematically blue-shift the dominant absorption peak.
results using the transition density plots. This helped us to differentiate the nature of the optical excitations. Our simulations allow us to extract the following conclusions: a) the key difference in the exciton dynamics of pristine (Zn intercalated) pentacene dimers is that in the former (latter) the exciton size increases (decreases) with the increasing intermolecule distances, b) Zn intercalation causes increasing overlap between the electron and hole states and enhances the generation of lowenergy charge-transfer excitons.
4. Conclusions
Declaration of Competing Interest
In summary, using the state-of-the-art TD-DFT technique, we investigate the optical excitations and exciton dynamics of pristine and Zn intercalated pentacene dimers as a function of the inter-molecule distances that vary in the range of 3 to 6 Å. We seek understanding of our
No conflict of interests to declare.
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Acknowledgement
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The research reported in this publication was supported by funding from Kuwait College of Science And Technology (KCST). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.cplett.2019.05.017. References [1] G.D. Scholes, G. Rumbles, Excitons in nanoscale systems, Nat. Mater. 5 (2006) 683 EP –, Review Article. [2] N. Kirova, Understanding excitons in optically active polymers, Polym. Int. 57 (2008) 678–688. [3] B.A. Gregg, Excitonic solar cells, J. Phys. Chem. B 107 (2003) 4688–4698. [4] Y. Tamai, H. Ohkita, H. Benten, S. Ito, Exciton diffusion in conjugated polymers: from fundamental understanding to improvement in photovoltaic conversion efficiency, J. Phys. Chem. Lett. 6 (2015) 3417–3428 PMID: 26269208. [5] S.M. Menke, R.J. Holmes, Exciton diffusion in organic photovoltaic cells, Energy Environ. Sci. 7 (2014) 499–512. [6] X. Zhang, Z. Li, G. Lu, First-principles simulations of exciton diffusion in organic semiconductors, Phys. Rev. B 84 (2011) 235208. [7] O.V. Mikhnenko, P.W.M. Blom, T.-Q. Nguyen, Exciton diffusion in organic semiconductors, Energy Environ. Sci. 8 (2015) 1867–1888. [8] J.-L. Brdas, J.E. Norton, J. Cornil, V. Coropceanu, Molecular understanding of organic solar cells: the challenges, Acc. Chem. Res. 42 (2009) 1691–1699 PMID: 19653630. [9] B.M. Savoie, N.E. Jackson, T.J. Marks, M.A. Ratner, Reassessing the use of oneelectron energetics in the design and characterization of organic photovoltaics, Phys. Chem. Chem. Phys. 15 (2013) 4538–4547. [10] C. Jundt, G. Klein, B. Sipp, J.L. Moigne, M. Joucla, A. Villaeys, Exciton dynamics in pentacene thin films studied by pump-probe spectroscopy, Chem. Phys. Lett. 241 (1995) 84–88. [11] J.H. Burroughes, D.D.C. Bradley, A.R. Brown, R.N. Marks, K. Mackay, R.H. Friend, P.L. Burns, A.B. Holmes, Light-emitting diodes based on conjugated polymers, Nature 347 (1990) 539–541. [12] J. Godlewski, M. Obarowska, Organic light emitting devices, Opto-Electron. Rev. 15 (2007) 179–183. [13] S. Sharifzadeh, P. Darancet, L. Kronik, J.B. Neaton, Low-energy charge-transfer excitons in organic solids from first-principles: the case of pentacene, J. Phys. Chem. Lett. 4 (2013) 2197–2201. [14] V.K. Thorsmølle, R.D. Averitt, J. Demsar, D.L. Smith, S. Tretiak, R.L. Martin, X. Chi, B.K. Crone, A.P. Ramirez, A.J. Taylor, Morphology effectively controls singlet-triplet exciton relaxation and charge transport in organic semiconductors, Phys. Rev. Lett. 102 (2009) 017401. [15] J.C. Slater, W. Shockley, Optical absorption by the alkali halides, Phys. Rev. 50 (1936) 705–719. [16] X. Liu, T. Pichler, M. Knupfer, M.S. Golden, J. Fink, H. Kataura, Y. Achiba, Detailed analysis of the mean diameter and diameter distribution of single-wall carbon nanotubes from their optical response, Phys. Rev. B 66 (2002) 045411. [17] B.M. Wong, T.H. Hsieh, Optoelectronic and excitonic properties of oligoacenes: substantial improvements from range-separated time-dependent density functional theory, J. Chem. Theory Comput. 6 (2010) 3704–3712 PMID: 21170284. [18] B.M. Wong, Optoelectronic properties of carbon nanorings: excitonic effects from time-dependent density functional theory, J. Phys. Chem. C 113 (2009) 21921–21927 PMID: 22481999. [19] S.A. Mewes, F. Plasser, A. Dreuw, Universal exciton size in organic polymers is determined by nonlocal orbital exchange in time-dependent density functional theory, J. Phys. Chem. Lett. 8 (2017) 1205–1210 PMID: 28230997. [20] S.A. Mewes, J.-M. Mewes, A. Dreuw, F. Plasser, Excitons in poly(para phenylene vinylene): a quantum-chemical perspective based on high-level ab initio calculations, Phys. Chem. Chem. Phys. 18 (2016) 2548–2563. [21] S.A. Mewes, F. Plasser, A. Dreuw, Communication: exciton analysis in time-dependent density functional theory: how functionals shape excited-state characters,
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Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
Charge-transfer excitons of metal intercalated pentacene dimers
T
Mufasila Mumthaz Muhammed, Aalyah Saqer Alotaibi, Fathima Alkhashman, ⁎ Junais Habeeb Mokkath Quantum Nanophotonics Simulations Lab, Kuwait College of Science And Technology, Doha Area, 7th Ring Road, P.O. Box 27235, Kuwait
H I GH L IG H T S
dynamics of technologically relevant organic systems is important for solar energy conversion. • Exciton TD-DFT, we investigate the exciton dynamics of both the pristine and zinc (Zn) intercalated pentacene dimers. • Using • Zn intercalation enhances the generation of low-energy charge-transfer excitons.
A B S T R A C T
The precise understanding of the exciton dynamics of technologically relevant organic systems is important for a plethora of applications, including solar energy conversion. Using state-of-the-art quantum chemical calculations based on time dependent density functional theory, we investigate the exciton dynamics of both the pristine and zinc (Zn) intercalated pentacene dimers as a function of the inter-molecular distances. We elucidate that the key difference in the exciton dynamics of pristine (Zn intercalated) pentacene dimers is that in the former (latter) the exciton size increases (decreases) with the increasing inter-molecule distances. Importantly, Zn intercalation causes increasing overlap between the electron and hole states and enhances the generation of low-energy charge-transfer excitons. We believe that our theoretical results are important for the emerging field of organic materials for solar-based applications.
1. Introduction An in-depth understanding on the exciton dynamics of organic semiconductors is imperative for improving the performance of organic solar cells [1–10] and light-emitting diodes [11,12], to list a few. It is well-known that the size and shape of the organic molecules strongly influences their exciton dynamics. Additionally, in the case of conjugated molecular systems, the exciton dynamics can be modified through stacking of the sub-units [13–16]. In a related context, it is reported that the charge-transfer state is energetically the lowest state of a conjugated molecular system. Consequentially, a higher lying excited state can efficiently relaxes to a charge-transfer state. In this context, state-of-the-art quantum chemical calculations have enhanced our understanding of organic molecules considerably by giving a firstprinciples description of the exciton dynamics [17–27]. In this paper, our goal is to elucidate the exciton dynamics of pristine and Zn intercalated pentacene (C22H14: five benzene rings joined in an armchair manner) dimers as a function of the inter-molecule distances. The choice of pentacene molecules is motivated by its rich exciton (coupled electron-hole pairs) physics [28]. Pentacene shows a strong Davydov splitting of the exciton spectra [29,30]. In
⁎
addition to being a classic organic semiconductor with high carrier mobility [31] pentacene is well-known for its propensity for singlet fission [32–34]. In this study, we show that Zn intercalation enables the emergence of charge-transfer excitons and their characteristics can be easily tuned by varying the inter-molecule distances. The paper is organized as follows. First, we describe the geometrical features of the investigated systems and the simulations methods employed. We show our results and discuss them in the next section, presenting a detailed analysis of the optical excitations and exciton dynamics. The conclusion and outlook section close the paper. 2. Computational aspects All calculations are performed with ORCA DFT/TD-DFT software (version 4.0) [35]. The geometry optimization of the single pentacene monomer was carried out using the b3-lyp exchange-correlation functional (non-local orbital exchange of 20%) [36] with dispersion corrections using Grimme’s DFT-D3 approach [37] and def2-TZVP basis set [38]. Further information regarding the DFT calculation parameters and/or the exchange correlation functional used is available in the ORCA manual. The SCF convergence was set to 10−8. A gradient
Corresponding author. E-mail address: [email protected] (J.H. Mokkath).
https://doi.org/10.1016/j.cplett.2019.05.017 Received 20 March 2019; Received in revised form 9 April 2019; Accepted 10 May 2019 Available online 13 May 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.
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convergence criterion of 10−6 and an energy convergence criterion of 10−6 were used in order to obtain well-converged pentacene monomer geometries. The optical spectra were computed using TD-DFT technique [39] in frequency space using b3-lyp functional. The choice of this hybrid exchange correlation functional is motivated by the fact that pentacene is well known to have rich excitonic physics. We found 100 roots are needed to compute the absorption spectrum up to an energy of 5.0 eV. All absorption spectra are broadened by Gaussian smearing of width σ = 0.10 eV. We seek understanding on the nature of the dominant peaks in the optical absorption spectrum using the transition density plots (it is a generalization of the transition dipole moment describing the transition between the Nth excited state and ground state) since they allow easy visual inspection of the optical excitations. The exciton analysis were performed with the theoDORE software [40,41]. The essence of the technique is to construct and analyze a twoparticle exciton wavefunction, which is given in terms of the positions and of the electron and hole quasi-particles. Further information regarding the calculation parameters is available in the theoDORE manual. An approximate exciton size (computed as the root-meansquare electron-hole separation) is calculated by using the following equation,
dexc =
∑MN
2 ΩMN dMN . Ω
Table 1 Optical gaps and exciton sizes of pentacene monomer, pentacene dimers, and pentacene dimers intercalated with Zn for d = 3, 4, 5 and 6 Å. System Pentacene Pentacene Pentacene Pentacene Pentacene Pentacene Pentacene Pentacene Pentacene
monomer dimer (d = 3 dimer (Zn) (d dimer (d = 4 dimer (Zn) (d dimer (d = 5 dimer (Zn) (d dimer (d = 6 dimer (Zn) (d
Å) =3 Å) =4 Å) =5 Å) =6
Å) Å) Å) Å)
Optical gap (eV)
Exciton size (Å)
2.10 2.20 1.86 4.25 1.67 4.21 1.80 4.17 1.80
5.56 5.83 5.52 6.23 5.92 7.06 4.74 7.84 4.30
particle transitions. Further insights into the aforementioned excitations can be obtained from their corresponding transition density plots, see Fig. 1. By inspecting the transition density plots, one can easily confirm that the 2.10 eV (4.0 eV) excitation exhibits the electron delocalization along the transverse (longitudinal) direction of the pentacene monomer. Table 1 shows that the calculated optical gap of the pentacene monomer is 2.10 eV. This is in agreement with the previous theoretical [optical gap of 2.20 eV using G0W0(PBE)] results [42] and experimental [optical gap of 2.30 eV using UV–visible spectroscopy] [43] results. The calculated exciton size of the pentacene monomer is 5.56 Å, see Table 1. Having discussed the nature of the optical excitations and exciton dynamics of the pentacene monomer, now we draw attention on pentacene dimers having inter-molecule gap distances (d) vary in the range of 3 to 6 Å, see Fig. 2. It should be recalled that when two or more monomers come into contact, not only do coupling between the excited states on each monomer have to be taken into account, but also chargetransfer states come into play. For example, in a dimeric system there are four states per type of monomer transition: a local excitation on each monomer and two charge-transfer states going in either direction. For small d values, all four states may couple to each other, producing highly complex mixed states [44]. Naively, it can be expected that more highly complex coupled states would emerge due to the Zn intercalation since a large number of possible local and charge-transfer states come into play. In addition, it is important to emphasize that the structure variations produce a marginal effect on the absorption profile, see Fig. S1 in the supporting information. Therefore, we believe that our model
(1)
where M and N are two atom indices, dMN is the distance between them and ΩMN is the probability of charge transfer from M to N. 3. Results and discussion Before discussing the optical excitations and exciton dynamics of the pristine and Zn intercalated pentacene dimers, it is instructive first to analyze the optical characteristics of the basic building blocks, i.e. the pentacene monomer. To this aim, we plot in Fig. 1 the optical absorption spectrum of the pentacene monomer in the energy range of 0 to 5.0 eV. The spectrum is characterized by two peaks centered at 2.10 eV [consists of 2 single-particle transitions, composed of HOMO→ LUMO (97%) and HOMO−2→LUMO+3 (3%)] and 4.0 eV [consists of 4 single-particle transitions, mainly composed of HOMO−2→LUMO (40%) and HOMO→LUMO+3 (31%)]. Note that 2.10 eV excitation is almost fully contributed by HOMO-to-LUMO transition, characteristic of an exciton. However, 4.0 eV excitation is composed of several single-
Fig. 1. TDDFT calculated optical absorption spectrum of pentacene monomer. Transition density plots corresponding to the excitations are also shown in Figure. Red and green color denote electron density accumulation (depletion) regions during the excitation, respectively. Both densities are plotted using the same iso-surface contour value. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 2. TDDFT calculated optical absorption spectrum of pentacene dimers as a function of d in the range of 3 to 6 Å. Transition density plots corresponding to the excitations are also shown in Figure. Red and green color denote electron density accumulation (depletion) regions during the excitation, respectively. Both densities are plotted using the same iso-surface contour value. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
respect to the d = 3 Å of the pristine pentacene dimer shown in Fig. 2). In particular, the spectral intensity of the strong excitation located between 4.0 and 4.5 eV is significantly reduced. The transition density plots corresponding to the different excitations depicts a mixed excitation. Note that this type of scenario is completely different for d in the range of 4 to 6 Å. In the case of d = 4 Å, one records the appearance of a low-energy excitation centered at 1.70 eV. The transition density plot corresponding to this excitation [mainly composed of HOMO→ LUMO (95%)] yields a charge-transfer exciton. It is important to mention that the small spectral intensity of the charge-transfer exciton results from the small spatial overlap of orbitals localized on individual pentacene monomers. The transition density plot corresponding to the strong excitation centered at 4.05 eV [consists of 10 single-particle transitions, mainly composed of HOMO−2→LUMO (42%) and HOMO−3→LUMO+3 (20%)] yields a local exciton confined to the individual pentacene monomers. Upon increasing the d value to 5 and 6 Å, one clearly observes significant modifications in the low-energy charge-transfer exciton. In particular, the inner region of the transition density plot becomes more closer to the intercalated Zn atom. This feature is highly pronounced for d = 6 Å since the inner region of the transition density plot becomes very much closer to the intercalated Zn atom. This results could have major implications on the exciton sizes. Table 1 shows that Zn atom intercalation causes sizable reduction of the exciton sizes [4 Å (5.92 Å) ⟶ 5 Å (4.74 Å) ⟶ 6 Å (4.30 Å)]. This is due to the fact that Zn intecalation enhances the interaction of the electron states of the individual pentacene monomers and affects the dynamics of the charge-transfer excitons. It is important to emphasize that the formation of charge-transfer excitons has strong implications in the singlet fission process where a photo-induced singlet excited state down-converts to two triplets, resulting in long-lived excitons and potential solar conversion quantum efficiencies exceeding 100% [46]. The efficacy of singlet fission depends sensitively on the nature of chargetransfer excitations, in the sense that electron and hole reside on different molecules, can accelerate singlet fission.
systems (two pentacene molecules with parallel orientations) and calculations will be valid as far as their optical response is concerned. Let us begin our analysis starting from the smallest considered d value of 3 Å. Apparently, one finds three excitations centered at 2.20 eV, 3.20 eV, and 4.30 eV, see Fig. 2. Transition density plots corresponding to the excitations are also shown in the figure. The transition density plot corresponding to the 2.20 eV peak [consists of 4 singleparticle transitions, mainly composed of HOMO→LUMO+2 (44%) and HOMO−1→LUMO+1 (36%)] depicts a local exciton confined to the individual pentacene monomers, whilst the 3.20 eV peak [mainly composed of HOMO−2→LUMO+1 (86%)] depicts a charge-transfer exciton, and 4.30 eV peak [consists of 12 single-particle transitions, mainly composed of HOMO−1→LUMO+10 (20%) and HOMO−6→ LUMO+3 (20%)] depicts a mixed excitation having a local and chargetransfer excitation components. It is noteworthy that for d = 4, 5, and 6 Å, there appears only one (strong and focused) excitation (located in the energy range between 4.0 eV to 4.5 eV) in the absorption spectrum and the low-energy excitations (present in the case of d = 3 Å) are completely vanished from the absorption spectrum. Apparently, the aforementioned strong excitation slightly red-shifts with the increasing d value in the range of 3 to 6 Å. Transition density plots corresponding to these peaks depict a mixed excitation. Now let us analyze the differences in the exciton size of pristine pentacene dimers as a function of the d values, see Table 1. The first remarkable observation is a uniform exciton size scaling (i.e. the growth of exciton size with the d) [45]. Specifically, for d = 3, 4, 5, and 6 Å, the calculated exciton sizes are 5.83 Å, 6.23 Å, 7.06 Å, 7.84 Å, respectively. After discussing the influence of inter-molecule distances on the optical excitations and exciton dynamics of the pristine pentacene dimers, we now present a similar analysis on Zn intercalated (in the geometrically central position between the monomers) pentacene dimers, see Fig. 3. The calculated results are cross-compared with the results shown in Fig. 2. In the case of d = 3 Å, one concludes that the effect of Zn intercalation is to slightly red-shift the excitations (with 3
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Fig. 3. TDDFT calculated optical absorption spectrum of pentacene dimers intercalated with Zn atom as a function of d in the range of 3 to 6 Å. Transition density plots corresponding to the excitations are also shown in Figure. Red and green color denote electron density accumulation (depletion) regions during the excitation, respectively. Both densities are plotted using the same iso-surface contour value. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. TDDFT calculated optical absorption spectra of pentacene dimers intercalated with Zn atoms in the range of 1 to 5 (d fixed to 4 Å).
Fig. 5. TDDFT calculated optical absorption spectra of pentacene dimers intercalated with Ca atoms in the range of 1 to 5 (d fixed to 4 Å).
We have examined the impact of Zn concentration (in the range of 1 to 5 atoms) on the pentacene dimer absorption profile (see Fig. 4), finding systematic developments in the spectral evolution. In addition, we have also examined the impact of other atomic species on the spectra evolution. To this aim, we chose calcium (Ca) atoms (relevant in hybrid organic/inorganic applications). Apparently, Fig. 5 shows that the key effect of increasing the Ca concentration is to systematically blue-shift the dominant absorption peak.
results using the transition density plots. This helped us to differentiate the nature of the optical excitations. Our simulations allow us to extract the following conclusions: a) the key difference in the exciton dynamics of pristine (Zn intercalated) pentacene dimers is that in the former (latter) the exciton size increases (decreases) with the increasing intermolecule distances, b) Zn intercalation causes increasing overlap between the electron and hole states and enhances the generation of lowenergy charge-transfer excitons.
4. Conclusions
Declaration of Competing Interest
In summary, using the state-of-the-art TD-DFT technique, we investigate the optical excitations and exciton dynamics of pristine and Zn intercalated pentacene dimers as a function of the inter-molecule distances that vary in the range of 3 to 6 Å. We seek understanding of our
No conflict of interests to declare.
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Acknowledgement
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