âWatchingâ Polaron Pair Formation from First-Principles Electron

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“Watching” Polaron Pair Formation from First-Principles Electron-Nuclear Dynamics Greta Donati, David B Lingerfelt, Alessio Petrone, Nadia Rega, and Xiaosong Li J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b06419 • Publication Date (Web): 29 Aug 2016 Downloaded from http://pubs.acs.org on August 30, 2016

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The Journal of Physical Chemistry

“Watching” Polaron Pair Formation from First-Principles Electron-Nuclear Dynamics Greta Donati,†,¶ David B. Lingerfelt,‡ Alessio Petrone,‡ Nadia Rega,∗,†,§ and Xiaosong Li∗,‡ †Dipartimento di Scienze Chimiche, Universit` a di Napoli ’Federico II’, Complesso Universitario di M.S.Angelo, via Cintia, I-80126 Napoli, Italy. ‡Department of Chemistry, University of Washington, Seattle, WA, 98195 ¶Current address: University of Washington,Department of Chemistry, University of Washington, Seattle, WA, 98195 §Italian Institute of Technology, IIT@CRIB Center for Advanced Biomaterials for Healthcare, Largo Barsanti e Matteucci, I-80125 Napoli, Italy. E-mail: [email protected]; [email protected] Phone: +39-081-674207; 206-685-1804

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Abstract The formation of polaron pairs is one of the important photophysical processes that take place after the excitation in semiconducting organic polymers. First-principles Ehrenfest excited state dynamics is a unique tool to investigate ultrafast photoinduced charge carrier dynamics and related non-equilibrium processes involving correlated electron-nuclear dynamics. In this work the formation of polaron pairs and their dynamical evolution in an oligomer of seven thiophene units is investigated with a combined approach of first-principles exciton-nuclear dynamics and wavelet analysis. The real-time formation of a polaron pair can be observed in the dipole evolution during the excited state dynamics. The possible driving force of the polaron pair formation is investigated through qualitative correlation between the structural dynamics and the dipole evolution. The time-dependent characteristics and spectroscopic consequences of the polaron pair formation are probed using the wavelet analysis.

Introduction Semiconducting organic polymers have a rich history in the development of alternative photovoltaics. 1–4 While advances in organic photovoltaic material’s power conversion efficiencies lag behind those of modern inorganic and mixed organic/inorganic materials, organic semiconductors are nonetheless an important class of materials that have unique advantages for certain applications due to their mechanical properties. The functionality and performance of organic materials strongly depend on molecular scale features that can be chemically modified to improve macroscopic properties and capabilities. Perhaps the most important process in determining the material’s characteristic charge carrier mobilities and transfer rates is the coupled, non-equilibrium electron-nuclear dynamics that follow photoexcitation. This process intimately correlates exciton dissociative (or charge separation) dynamics with structural skeletal changes induced in the molecule along particular vibrational modes. Therefore, the exciton diffusion and dissociation rates can be modulated by excitonic coupling to intrin2


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sic vibrational modes and the presence of photo-induced self-trapped 5 states (i.e. polaron pairs). 6–16 In some condensed materials where electron and hole can be trapped independently, single polaron can also be formed. 17 A fundamental understanding of these coupled exciton-nuclear dynamics is crucial to improving the performance of semiconducting organic polymers. However, the detailed physical processes and consequential observations arising from the coupled excited-electron-nuclear dynamics lack accurate theoretical descriptions. The formation of polaron pairs is one of the possible photophysical processes that can take place after the excitation. Recent works suggest that polaron pair formation plays a significant role in photovoltaic action, and polaron pair dynamics are nowadays considered to be as important as those of ‘bare’ excitons. 18–20 Moreover, an important feature of both excitons and polaron pairs is the strong dependence of their dynamical properties on the structural dynamics of the polymers. 21–24 This feature permits these pseudo-particles’ study by techniques such as Raman spectroscopy, because structural information can be probed to deduce the polaron pairs’ formation and dynamics. 21,25,26 In fact, the role played by the dynamics of polaron pairs in the poly(3-hexylthiophene) has been studied by various timeresolved excited state spectroscopies, confirming the importance of the structural feature for the polaron pairs dynamics. 18,21,26–28 Even with advanced time-resolved spectroscopic techniques, the mechanistic underpinnings of the experimental observations are still difficult to resolve without cross-correlating spectroscopic signals of electronic and vibrational degrees of freedom. From the theoretical modeling standpoint, the main challenge is presented by the complex multi-scaled timeevolution of a fast-evolving electronic wave function coupled to the slower non-equilibrium nuclear dynamics. 29 In this work, the first-principles Ehrenfest dynamics 30–34 is used in concert with multiresolution vibrational analysis based on the wavelet transform, 35–40 to simulate and characterize the chemical dynamics following photoexcitation of a regioregular alkylthiophene oligomer. This coupled electronic-nuclear dynamics approach accurately reproduces the ultrafast non-equilibrium chemical dynamics to properly simulate polaron

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pair formation, and at the same time also permits analysis of the molecular dynamics in terms of both the charge carrier evolution and structural rearrangements. In addition, the wavelet analysis retains temporal information lost with standard Fourier analyses, allowing the identification of important structural rearrangements with both spatial and temporal resolution.

Methodology The first-principles Ehrenfest dynamics in the atomic orbital basis 30–33 was employed in this study to investigate the formation of a polaron pair and its evolution in a regioregular 3-methylthiophene oligomer comprised of seven monomers. The non-adiabatic nature of this method is needed to investigate photoinduced processes that potentially involve energy transfer between electronic and nuclear degrees of freedom. As the ab initio Ehrenfest dynamics method has been previously developed and applied to modeling various ultra-fast excited state electron-nuclear dynamics, we provide only a brief description of it here. In the first-principles Ehrenfest dynamics implementation, the electronic degrees of freedom are propagated with real-time time-dependent density functional theory (RT-TDDFT) while the electron-nuclear interactions responsible for the electronically non-adiabatic time evolution are modeled with the Ehrenfest technique, which propagates the nuclei on the time-evolving electronic potential. The Ehrenfest dynamics scheme employed in this work takes advantage of an efficient, triple-split operator integrator. These different time steps reflect the characteristic timescales of the three different molecular equation-of-motion integrators: nuclear motion driven by the velocity-Verlet algorithm 41 with a time-step of ∆tN , evolving time-dependent Kohn-Sham Hamiltonian with a time-step of ∆tN e , and a unitary transformation RT-TDDFT with a time-step of ∆te employed to propagate the electronic degrees of freedom. For a detailed description of the current implementation, we refer readers to Refs. 30 and 33.

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The non-stationary signals collected during the electron-nuclear dynamics were resolved via the multi-resolution continuous wavelet analysis protocol. 35–39 This protocol has been successfully proposed previously for the analysis of non-equilibrium trajectories 40 to track vibrational contributions beneath time-dependent spectroscopic observable signals in the frequency domain without losing their temporal information. Briefly, a wavelet transform is an integral transform in the same spirit as the Fourier transform, W (a,b) =

Z

F (t)ψa,b (t)dt

(1)

where F (t) is the signal extracted from the trajectory, and the wavelet functions ψa,b (t) are obtained as stretched and translated versions of a chosen “mother” wavelet. In this way a family of wavelet functions is generated from a mother wavelet by changing two parameters: the scale a, proportional to the inverse of frequency, and the translation parameter b, which determines the wavelet’s position along the temporal axis:

ψa,b (t) = |a|

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t-b (a, b ∈ R; a 6= 0) ψ a

(2)

The wavelet transform is sensitive to the different frequency content present in the signal at a given time because the a parameter allows the wavelets to be stretched or compressed to adapt to the signal’s frequency content. The wavelet functions are also freely translated in time through the b parameter, allowing for the temporal localization of transient frequencies. In this work, we chose the Morlet function 42 as mother wavelet. The wavelet power spectra are obtained by plotting |W (ν, t)|2 , which is the time-dependent intensity of a frequency ν contributing to the F (t) signal at time t. All calculations, including geometry optimizations and linear-response TDDFT treatment of the excited states, were performed at the CAM-B3LYP 43 /6-31G(d) theory level using a development version of the Gaussian suite of programs. 44 The choice of this level of theory is based on several computational studies that demonstrated accurate results for studies of

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ature (298 K). For a specific vibrational mode with a given Boltzmann-sampled vibrational energy, the initial phase was chosen randomly and classically. 52,53 Note that the motivation of this work is to illustrate the formation of a polaron pair and its spectroscopic consequence, rather than to investigate the statistical thermodynamics of a particular excited state ensemble. Therefore, we chose a single initial condition with the most planar arrangement, which gives rise to the most delocalized electronic distribution, to “track” the polaron pair formation dynamics. The initial excited state electronic density was prepared by promoting one electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) (see Fig. 1). This is the dominant orbital pair in the S0 → S1 excitation, according to the linear-response TDDFT calculations. The three time steps in the Ehrenfest dynamics simulation are ∆tN = 0.1 fs, ∆tN e = 0.01 fs, ∆te = 0.001 fs. The total energy conservation is within 0.02 kcal/mol. We also performed an ab initio Born-Oppenheimer molecular dynamics (BOMD) 54 simulation in order to compare the polaron pair formation dynamics to the structural dynamics of the system in the ground electronic state. The initial nuclear coordinates and momenta of the BOMD dynamics are the same used for the Ehrenfest dynamics. The Ehrenfest trajectory was collected for about 90 fs while the BOMD for about 1.7 ps. The harmonic vibrational analysis was performed on the ground state minimum energy structure in both the ground and the first singlet excited state, where in this last case vibrational frequencies were calculated numerically.

Results and Discussion The electronic structure of the photo-excited 3-methylthiophene can be described by the dominant HOMO → LUMO transition. These frontier orbitals, as shown in Fig. 1, are delocalized, suggesting that photoexcitation does not directly lead to instantaneous polaron

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pair formation. One has to probe the interplay between time evolution of excited electronic states and molecular structure to understand the mechanistic driving force of polaron pair dynamics.

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Figure 2. (a) Total dipole moment temporal evolution of 3-methylthiophene heptamer during the Ehrenfest excited state dynamics. (b) Total dipole moment temporal evolution of 3-methylthiophene heptamer during the ground state BOMD simulation. Red: instantaneous dipole moment for every ∆te = 0.001f s or ∆tN = 0.1 fs for the Ehrenfest or BOMD simulations, respectively. Black: time-averaged dipole moment over 5 fs.

Figure 2a shows the temporal evolution of the total dipole moment of the photo-excited state during the Ehrenfest dynamics, collected every electronic time step (∆te ) and timeaveraged over every 5 fs. For a two-state system without dissipation or change in potential energy surface, the excited dipole moment will oscillate between those of the ground- and excited states with a simple frequency that corresponds to the excitation frequency. 55 However, convoluted with the oscillatory behavior of the dipole in Fig. 2a is an underlying trend clearly characterized by several regions in which the excited-state dipole moment exhibits different signatures. Within 10 fs of the excitation there appears to be an oscillatory behavior of the time-averaged dipole magnitude between ∼1.8 D and ∼10 D. This oscillatory behavior stops at ∼12 fs, at which point a constant dipole moment of ∼5 D is observed and maintained until 30 fs. After 30 fs a quick decrease of the dipole takes place until around 38 8


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fs. This event initiates the second long period of time in which the dipole retains, on average, constant values around 2.5−3 D until 50 fs. The third and final period is characterized by average oscillations around 2 D that persist until the end of the dynamics. The analogous total dipole evolution is reported for the ground state Born-Oppenheimer molecular dynamics (BOMD) in Fig. 2b. In contrast to the characteristics of the time-dependent dipole moment in Fig. 2b, the ground state dynamics only gives rise to dipole oscillations between 0.5 D and 2.5 D, simply due to molecular structural changes. Analysis of the time-dependent dipole suggests that the excitation is responsible for a charge separated state in the system that is not observed in the ground state. The observed periods of dipole plateaus in Fig. 2a suggest that electron-hole pair separation/recombination is temporarily trapped during the exciton-nuclear dynamics. In this trap state, the charge carriers’ delocalization pathway is blocked, and the decay of timedependent dipole is quenched. This can only arise from structural deformations induced by the charge carrier dynamics, creating short-lived exciton-vibrational trap states, or polaron pairs. In other words, we have observed the signature of polaron pair formation in Fig. 2a.

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x y z

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Figure 3. (a) Time evolution of dipole moment components of 3methylthiophene heptamer during the Ehrenfest dynamics. (b) Time evolution of dipole moment components of 3-methylthiophene heptamer during the BOMD simulation.

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Figure 3 plots the time-evolutions of dipole components from the exciton-nuclear dynamics (Fig. 3a) and the ground state dynamics (Fig. 3b). As shown in Fig. 3b, all three dipole components from the ground state dynamics do not show significant changes. In contrast, in the exciton-nuclear dynamics (Fig. 3a), there is a dominant contribution from the dipole component along the polymer chain (x direction), compared to the other two components (dipole along the shortest axis in the polymer plane, y, and the out-of-plane axis, z ). As the main contribution to the total dipole moment, the time-dependent characteristics of the x component follows the trend observed in Fig. 2a, i.e. periods of dipole plateaus. The dipole analyses suggest that polaronic states can be formed after the excitation. The polaron pair formation can be observed by monitoring both the charge carrier and structural parameters’ evolution during the excited state dynamics. At this point it is interesting to understand the molecular properties that are associated with the creation of these polaron states. We turn now to analysis of the structural dynamics and look for correlation between excitonic dynamics observed in Fig. 2a and the molecular structural dynamics. 180

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Figure 4. Time evolution of S-C-C-S dihedral angles of 3-methylthiophene heptamer during the Ehrenfest (left panel) and BO (right panel) dynamics (see Fig. 1 for ring indices).

The stepped decay in the extent of charge separation following the photoexcitation can be interpreted in light of structural reorganizations when both analyses are performed in 10


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the time domain. Figure 4 shows the time-evolution of the oligomer intermolecular dihedral angles S−C−C−S, which measure the degree of planarity of the system, in the excited state Ehrenfest dynamics (left panel). A close examination reveals a strong correlation of motion between the dihedral dynamics in the excited state and that of dipole moment observed in Fig. 2a. A careful comparison of the time-dependent x, y and z components of the dipole reveals that changes in x component are synchronized with the slow profile oscillations of the y and z components. This suggests that the polaron pair formation may be a result of structural changes along the y and z directions, i.e. the polymer backbone out-of-plane motion. This interesting mechanism is specific and characteristic of conjugated polymers in which the torsional motions can break the conjugation and block the exciton delocalization pathway causing a charge trapping. In greater detail, the dihedral angle 6−7 after the first 20 fs assumes values closer to planarity. Starting from around ∼125 degrees, it reaches ∼140 degrees and retains this degree of inter-ring torsion for a period of about 30 fs. Later it gradually returns to its initial value. This structural trend is correlated to the 4−5 dihedral angle, but in this case the behavior is the opposite. The 4−5 dihedral starts nearly planar at ∼165 degrees, and begins to deviate from planarity after 20 fs approaching to ∼140 degrees. It exhibits the same dynamics as the 6−7 dihedral angle by retaining the same value for about 30 fs. Such a concurrence of dihedral angle motions supports step-wise localization of charges as the out-of-plane vibrations break the conjugation between adjacent monomer rings. One can also observe correlations between the step-wise dipole dynamics and other dihedral angle’s motions. For example, the 5−6 dihedral angle shows almost constant values around −145 degrees, but after 50 fs it starts deviating from planarity until reaching values around −130 degrees. This motion correlates to the generation of the last step-wise dipole moment decrease in Fig. 2a. Comparing the time evolutions of dihedral angles in the excited and ground states (left

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and right panels of Fig. 4, respectively), it is clear that the correlation found in the excited state dynamics is absent in the ground state dynamics, suggesting that the correlated rings motions are related to the polaron pair dynamics. The correlation between the charge separation and the out-of-plane motions is understandable and well-established in the literature because the conjugation and electron delocalization strongly depend on the planarity of the structure. The out-of-plane motions can trap the exciton and prevent it from freely recombining/diffusing. When the planarity of adjacent monomers deviates from ideal conjugated structure, time-evolving electron density can be trapped in a few monomer rings, and polaron pairs are formed and quickly decay with a lifetime of ∼10 fs as seen from Fig. 2a. Previous discussion focused on analyzing the structural dynamics correlated with polaron pair formation in the model organic polymer. We now turn our investigation of structural parameters to the frequency domain by focusing on the other geometric parameters strongly affected by the polaron pair formation: the C−C bonds vibration temporal evolution. The temporal frequencies and intensities of time-evolving total dipole moment have signatures of the polaron pair formation. Analysis of these signatures may provide important insights into the geometric parameters that are strongly affected by the polaron formation. In Fig. 5 the wavelet spectrum in the range of 1000 to 2000 cm−1 of the total dipole moment is presented. This spectral region is characterized by a main band centered around 1500 cm−1 . Harmonic vibrational analysis on the excited state indicates that this band is associated with the intra-ring C−C stretching modes of the thiophene rings. This band appears immediately after the excitation, followed by a considerable decrease in intensity at about 20 fs. This behavior is coincident with what observed in the dipole time-evolution in Fig. 2a, suggesting a correlation between the polaron pair formation and intra-ring C−C stretching mode. To investigate further, we considered the dynamics of a C−C bond as a local interrogation of the evolution of C−C stretching modes. According to the harmonic vibrational analysis on the excited state, C−C bond stretching motions contribute to intra-ring C−C stretching

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Time (fs) Figure 7. Temporal evolution of the maximum frequency extracted from the Wavelet power spectra of the Ca −Cb bond distance temporal evolution during the Ehrenfest excited state dynamics.

bond takes place around that time, likely due to the polaron migration. Figure 7 plots the temporal evolution of the frequency corresponding to the maximum amplitude of the wavelet analysis of the Ca −Cb bond stretching. Immediately after the photoexcitation, the vibrational frequency of the Ca −Cb is red-shifted compared to that in the ground state. Such a red-shift is a result of the π → π ∗ transition that leads to weakening of the bond. At ∼50 fs, the Ca −Cb vibrational frequency starts to blue-shift towards the ground state value, coincident with recovery of the planarity as suggested by the motion of 6-7 dihedral angle (Fig. 4). This observation suggests that a polaron is formed at the 7th ring following photoexcitation. As the polaron is displaced from the Ca −Cb region, the bond stretching frequency recovers towards that of the ground state, accompanied with the dipole approaching that of the ground state (Fig. 3a). These phenomena have been observed in time-resolved Raman spectroscopy experiments in which red-shifts of the C−C vibrational bands are associated to the presence of polaron pairs in the polymer. 28 The ability to reliably infer the ultrafast photoinduced charge carrier dynamics from timedependent shifts of certain vibrational features provides experimentalists with an important tool to investigate these, and related non-equilibrium processes involving dynamically cor-

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related electron-nuclear processes. More generally, the evolution of frequency and intensity of C−C stretches can be exploited as a local probe of the photoinduced increase of planarity in oligo- and poly-thiophenes, as recently shown by femtosecond stimulated Raman experiments. 26,28,48

Conclusion In this paper we investigate the formation of polaron pairs and their dynamical evolution in an oligomer of seven thiophene units as a model for regioregular and alkyl-substituted thiophene polymers widely employed in photovoltaic devices. A combined approach of firstprinciples exciton-nuclear dynamics and wavelet analysis is employed to track the real-time formation of a polaron pair. The dynamical evolution of the polaron pair can be monitored, characterizing both in a qualitative and quantitative way the charge density changes upon the excitation. Further evidence for the polaron pair formation is provided by the closely correlated charge carrier and structural dynamics, analyzed in both the time and the frequency domain through the mutiresolution wavelet analysis. In particular, the correlation between the step-wise decay of time-dependent dipole and the dynamics of S−C−C−S dihedral angles suggests that the formation of a polaron pair is modulated by the out-of-plane motion of the polymer backbone dynamics. When the planarity of adjacent monomers deviates from ideal conjugated structure, time-evolving electron density can be trapped in a few monomer rings, forming a polaron pair. The observed lifetimes of such trapped polarons are ∼10 fs from the exciton-nuclear dynamics. Utilizing the wavelet analysis method allows one to give a spectroscopic point of view on the phenomena taking place during the polaron dynamics. The wavelet spectra of the dipole dynamics in the 1000-2000 cm−1 range reveal characteristic changes of C−C stretching modes consisting of combinations of intra-ring local C−C vibrations. The exciton-nuclear dynamics

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is also studied through the time-resolved vibrational spectra of prominent C−C stretches using the multiresolution wavelet analysis to resolve their non-equilibrium temporal signals. The C−C bond stretching frequency is red-shifted compared to that in the ground state. This is due to the formation of a localized polaron. As the polaron migrates, the C−C bond stretching frequency recovers towards that in the ground state. The wavelet analyses strongly suggests that the polaron pair dynamics can be monitored by structural parameters and also by spectroscopic investigations that are sensitive to the temporal evolution of these geometric deformations. Both the shifts of these vibrational bands and the inter-ring rearrangements are correlated to the polaron pair dynamics as also suggested by experimental results. 18,26,28

Acknowledgement The development of the first-principles Ehrenfest dynamics is supported by the US Department of Energy (DE-SC0006863). The educational outreach and international scientific collaboration is supported by the National Science Foundation (CHE-1565520). The University of Washington Student Technology Fund provided computational resources to enable this work.

Supporting Information Available This material is available free of charge via the Internet at http://pubs.acs.org/.

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