Impurity Effects on Excited-State Dynamics of Conjugated Polymers

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C: Energy Conversion and Storage; Energy and Charge Transport

Impurity Effects on Excited-State Dynamics of Conjugated Polymers Zhen Sun, Sheng Li, Shijie Xie, and Zhong An J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b04380 • Publication Date (Web): 13 Aug 2019 Downloaded from pubs.acs.org on August 13, 2019

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The Journal of Physical Chemistry

Impurity Effects on Excited-State Dynamics of Conjugated Polymers Zhen Sun,∗,† Sheng Li,† Shijie Xie,‡ and Zhong An¶ †Department of Physics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China ‡School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, 250100, China ¶College of Physics, Hebei Normal University, Shijiazhuang 050024, China E-mail: [email protected]

Abstract The influences of impurity on excited-state dynamics of a single polymer chain are investigated relying on Tully’s fewest switches surface hopping (FSSH) method. The method is based on Pariser-Parr-Pople (PPP) Hamiltonian and excited-state calculations at configuration interaction singles (CIS) level. The results show that impurity doping removes the restriction of jumping between exciton (EX) type and charge transfer (CT) type excited state in pristine polymer chain. The jumping from an EX-type excited state to a CT-type excited state could trigger the exciton dissociation process. Impurity doping breaks the electron-hole symmetry of excited-state wavefunctions and induce electron-hole separation to some degree. Through changing the strength of nonadiabatic couplings between excited states, the impurity can significantly reduce the lifetime of an excited state.

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Introduction Conjugated polymers have shown great potential applications in optoelectronic devices, such as light-emitting diodes (OLEDs) and organic solar cells (OSCs) 1 . Excited-state dynamics of conjugated polymers are involved in a lot of photophysical processes, such as exciton formation and dissociation 2 , polaron pair recombination 3,4 , and exciton-polaron quenching 5 . Understanding and then controlling the excited-state dynamics should be crucial to improve the performance of conjugated polymers in these applications. A conjugated polymer chain usually contains hundrads of atoms. In order to study the excited-state dynamics of such a system, people generally have to adopt severe approximations. An et al. have performed Ehrenfest molecular dynamics simulations on a single polymer chain to address the mechanism of charged polaron generation. 6 Their method is based on Su-Schrieffer-Heeger (SSH) Hamiltonian where the excited states are described using Huckel molecular orbits. Later, Miranda et al. performed the same simulations using Ehrenfest method which is based on Pariser-Parr-Pople (PPP) Hamiltonian where the excited states are constructed by only two electron configurations of single excitations with fixed coefficients 7,8 . Although Ehrenfest method has achieved great success to a number of problems, it has some limitations due to its mean-field character 9 . When a polymer chain is initially populated to a pure adiabatic state, it will be in a mixed state afterwards. The mixed state is unable to describe different excited-state evolution channels adequately. Recent years, the fewest switches surface hopping (FSSH) method, described by Tully in 1990, 10 has been widely used and is still in rapid developing. 11,12 In the FSSH method, the system is always propagated on a pure adiabatic state, and an algorithm is designed to allow the system switch between adiabatic states. The surface hopping technique needs evolve an ensemble of trajectories. The computational cost of FSSH simulations mainly depends on the level of excite-state calculations and the system size. In order to deal with relatively large systems, configuration interaction singles (CIS) and time-dependent density function theory (TDDFT) are commonly used to describe excited state in surface hopping 2


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method. 13–15 Using the FSSH method, the excited-state dynamics of conjugated polymers, such as oligomers of poly-(phenylene ethylene) (PPV) and thiophene, have been studied by several groups, including Rossky and co-workers 16–18 , Tretiak and co-workers 19 , Barbatti and co-workers 20 . The FSSH method becomes one of the most popular methods in the field of excited-state dynamics. Classification on excited states of conjugated polymers can enhance our understandings on the properties of excited states. Köhler et al. 21,22 found that the first five excited-state wavefunctions of PPV which correspond to five peaks in the absorption spectrum can be divied into two types: for type one, the electron and hole are significantly bound together and have small coherence size, and for type two, the electron and hole are separated by a few phenylene rings and have large coherence size. Bittner et al. 23 studied the excited states of various conjugated polymers and pointed out that the excited states can be divided into two types due to the even or odd symmetry of electron/hole wavefunctions under spatial inversion. The even-parity states are dominated by geminate electron/hole configurations and usually have strong optical coupling to the ground state, while the odd-parity states are charge-separated states and usually have weak optical coupling to the ground state. In our previous work, we also classify excited states of a single polymer chain, including singlet and triplet, into two types: exciton (EX) type and charge transfer (CT) type, according to whether the diagonal elements of their transition density matrices being zero or not 24 . Because the transition densities, expressed by the diagonal elements of transition density matrix, of CT-type excited states equal to zero, all CT-type excited states are completely “dark”. Thus, the polymer chain is always photoexcited into a singlet EX-type excited state. In general, in EX-type excited state the electron and the hole are tightly binding, while in CT-type excited state the electron and the hole are loosely binding. Moreover, we found that the nonadiabatic couplings between EX-type excited state and CT-type excited state keep zero all along during evolution 25 . Because of this, the system will remain in EX-type excited state after it is photoexcited into a high-lying EX-type excited state. However, whether

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impurity can remove this restriction still remains an open question. To the best of our knowledge, the impurity effects on excited-state dynamics of conjugated polymers are still a missing feature in this research field. In the current work, we use the FSSH method to investigate how an impurity affects the relaxation process when a single polymer chain is photoexcited to a high-lying excited state. We also address the electron and hole movement in real space and their separation during this relaxation process. Through these investigations, we hope to obtain comprehensive understandings on the nature of excited-state dynamics in conjugated polymers, and then contribute to their applications.

Methods We consider a single polymer chain with an impurity at the middle of the chain. The overall Hamiltonian of this polymer chain is described as

H = Helec + Himp + Hlatt ,

(1)

where Helec , Himp , and Hlatt correspond to electron, impurity and nuclei components, respectively. Helec is written by the PPP Hamiltonian 26

Helec = −

X

tµ,µ+1 (c†µ,s cµ+1,s + c†µ+1,s cµ,s ) + U

X

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µ

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1 1 (nµ↑ − )(nµ↓ − ) + 2 2 (2)

µ,ν

where c†µ,s and cµ,s are the creation and annihilation operators for a π electron with spin s at P site µ, nµ = s c†µ,s cµ,s , the total number of electrons on site µ. The nearest hopping integral tµ,µ+1 = t0 − α(rµ,µ+1 − r0 ) + (−1)µ+1 te , where t0 is the hopping integral for equal intersite distances r0 , rµ,µ+1 ≡ |xµ − xµ+1 | the distance between neighbor sites, α the electron-phonon coupling constant, and te the extrinsic transfer term, introduced to lift the ground state degeneracy. U and Vµν are the on-site and inter-site Coulomb interactions, respectively. 4


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The Vµν are obtained from a modification of the Ohno parameterization Vµν = U/κ(1 + 1

2 2 ) , where κ denotes an effective dielectric constant. The impurity component Himp 0.6117rµν

describe an on-site impurity which is located on the middle of the chain 27,28 . It is written by

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s

where Vimp is the strength of the impurity, and site N is chain length. The nuclear component Hlatt is written by

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KX (rµ,µ+1 − r0 )2 , 2 µ

(4)

where K is the elastic constant. The values of parameters in above equations are set as: t0 = 2.0 eV, α = 4.0 eV/Å, r0 2

= 1.50 Å, K = 45.0 eV/Å , te = 0.05 eV, N = 20. The values of parameter U and κ are set 8.0 eV and 2.0, respectively, derived by Chandross and Mazumdar. 29 In the FSSH method, the wavefunction of electronic system is expressed by a linear P s combination of the CIS states Φ(t) = N I cI (t)φI , where {φI } are the CIS eigenvectors of the electronic Hamiltonian Helec . Substitute the expression into the time-dependent Schrödinger equation, we obtain N

s X dcK (t) i = − EK (t)cK (t) − cI (t)σKI (t), dt h ¯ I=1

(5)

I where EK is the CIS eigenvalue of Helec , σKI = hφK | ∂φ i, the nonadiabatic coupling (NAC) ∂t

term between electronic state K and I, with σKK = 0, σKI = −σIK . The nuclei are propagated along a classical trajectory, according to the Langevin equation of motion, 30

M x¨µ (t) = −

K dEtot − γM x˙ µ (t) + ζ(t), dxµ

5


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K where Etot is the total electronic and lattice energy of K-th excited state, M , x¨µ and x˙ µ

represent the mass, acceleration and velocity of the µth site, respectively. The stochastic force ζ depends on the bath temperature T and the friction coefficient γ. It obeys the fluctuation-dissipation theorem satisfying the condition: < ζ(t)ζ(t+∆t) >= 2M γkB T δ(∆t). In this work, the bath temperature T is set to 300 K. Following Tully’s FSSH algorithm, the switching probability from the currently occupied excited state K to another excited state I is PNq Re[cK c∗I ] j=1 σKI δt , = ∗ cK cK

gKI

(7)

where Nq is the number of quantum steps per classical step, δt the quantum step. The details of the FSSH method can be found in our previous published paper and its supporting information 25 . The initial site coordinates and velocities are generated by taking snapshots every 0.2 ps from an adiabatic molecular dynamics running on the ground state at T=300 K after the polymer is equilibrated. In order to characterize the excited states of the polymer chain, we use the normalized transition density matrix

QIµν

P Ia ia Cµi ti Cνa | P , Ia µν | ia Cµi ti Cνa |

| =P

(8)

where tIa i is the CIS coefficient of I-th excited state and Cµa the molecular orbital (MO) coefficient 31 .

Results and Discussion At first, let’s see the impurity effects on the excited-state wavefunctions of the single polymer chain. Fig. 1 shows the contour maps of the transition density matrices QIµν for the lowest eight singlet excited states of the polymer chain. The top two rows (S1 - S8 ) are for the pristine

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S 8

2 4 6 8 10 12 14 16 18 20 site

Figure 1: The contour maps of the normalized transition density matrices QIµν of the lowest eight excited states. The top two rows (S1 - S8 ) are for the pristine polymer chain, and the bottom two rows (S01 - S08 ) for the impurity doped polymer chain with Vimp = −0.5 eV.

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polymer chain, and the bottom two rows (S01 - S08 ) for the impurity doped polymer chain. These transition density matrices are calculated using one of the initial lattice configurations which are prepared for surface hopping simulations. The transition density matrix of an excited state actually reflects the electron and the hole distribution probabilities in real space. The diagonal elements QIµµ represent the transition density on the µ-th site when the polymer undergoes the transition from ground state to the I-th excited state, whereas the element QIµν (µ 6= ν) represents the joint probability of finding an electron on site µ and a hole on site ν. For the pristine polymer chain, as we have discussed in our previous work 24 , the excited states from S1 to S8 can be classified into two types: EX-type and CT-type, according to whether the diagonal elements of their transition density matrices being zero or not. If the diagonal elements of transition density matrix of an excited state exactly equal to zero, it belongs to CT-type. If they do not, it belongs to EX-type. Actually, this classification applies to all excited states, including both singlet and triplet. By definition, EX-type excited states include S1 , S3 , S5 , and S6 , and CT-type excited states include S2 , S3 , S7 , and S8 . Now we discuss the symmetry of the distributions of excited states from S1 to S8 . We take state S1 for example. Other excited states have the same symmetries with state S1 . The distribution of state S1 is biased towards to the left bottom, which means that the exciton occupies the left of the chain (the site is numbered from the left to the right of the chain). The exciton does not occupy the middle of the chain, i.e., the distribution does not show symmetry with respect to the secondary diagonal, because the lattice configuration is not in perfect dimerization. The lattice configuration of the chain is randomly chosen from the initial site coordinates prepared for surface hopping simulations. Due to the lattice thermal vibration, the central symmetry of the chain is broken. However, the distribution of state S1 shows perfect symmetry with respect to the leading diagonal, i.e., QIµν = QIνµ . That is to say, the electron and the hole remain symmetric. This electron-hole symmetry indicates that the electron and the hole wavefunctions exactly overlap each other, and there is no excess

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charge everywhere on the chain. For the impurity doped polymer chain, the distribution patterns of excited states from S01 to S08 look like their counterpart of pristine polymer chain, except for S05 and S06 . Also, it seems that they can be classified into EX-type and CT-type. Actually, if we check the diagonal element values of the transition density matrices of excited states like CT-type, they do not exactly equal to zero, but they are very small. We can call them quasi CT-type excited states. Moreover, the distributions from S01 to S08 no longer show symmetry with respect to the leading diagonal, i.e., QIµν 6= QIνµ . That is to say, the electron-hole symmetry is broken. Obviously, this broken electron-hole symmetry is due to the introduction of impurity. In this situation, the electron and the hole wavefunctions do not exactly overlap, and the excess charge should appear somewhere on the chain. In the following, we will see that this broken symmetry will induce great changes in the nonadiabatic couplings between excited states and electron-hole separation. In the following, we will study the excited-state dynamics after the system is photoexcited to the lowest three EX-type excited states S6 , S5 and S3 , respectively. Let’s first check the NAC terms when the system is evolving on state S6 . Because of the relation σIJ = −σJI , there are 15 unknown NAC terms in total between the lowest six excited states. When calculating these NAC terms at each time step, we turn off the hopping mechanism in a surface hopping simulation for a typical trajectory. The time dependence of all these fifteen NAC terms are shown in Fig. 2. In order to see the impurity effects on NAC terms, panel A is for the pristine polymer chain, and panel B for the impurity doped polymer chain. For the pristine polymer chain, we see that some NAC terms oscillate with time, and the rest of NAC terms keep zero throughout time evolution. The oscillations in NAC terms are aroused by the C-C bond stretching. Combined with the above discussions on the classification of excited states (as shown in Fig. 1), it is found that all NAC terms which remain zero throughout time evolution are between EX-type and CT-type excited state. This means that EX-type excited state never interacts with CT-type excited state. In other words, if the

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Figure 2: Nonadiabatic coupling terms as a function of time when the system is restricted to evolve on state S6 . Panel A is for the pristine polymer chain, and Panel B for impurity doped polymer chain with Vimp = −0.5 eV. 10 ACS Paragon Plus Environment

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system is excited to an EX-type excited state, it only can jump to other EX-type excited states, but cannot jump to any CT-type excited states. Otherwise, we find that NAC term σ65 is tremendously stronger than other NAC terms. This means that the system will have very high probability of jumping from state S6 to S5 . From panel B of Fig. 2, we see that there are no NAC terms which remain zero throughout time evolution. That is to say, when an impurity is introduced into the polymer chain, the NAC terms that remain zero in case of pristine polymer chain are no longer zero. This means that the restriction of jumping from EX-type excited state to CT-type excited state is removed. We further study the time evolution of NAC terms when the system is restricted to evolve on state S5 . In this case, we still check the 15 unknown NAC terms between the lowest six excited states, as shown in Fig. 3. Fig. 3 A showes the NAC terms σIJ for the pristine polymer chain, and Fig. 3 B for the impurity doped polymer chain. For the pristine polymer chain, we again find that some NAC terms oscillate and the rest of NAC terms remain zero throughout time evolution. Similarly, all NAC terms which remain zero are between EX-type excited state and CT-type excited state. Here, we notice that NAC term σ65 in Fig. 3 A(b) is not as strong as that in Fig. 2 A(b). This is because when the system is evolving on state S5 the energy level of state S5 is pressed down, which increases the gap between state S5 and S6 , and then the NAC between them is weakened. Likewise, when the system is evolving on state S6 the energy level of state S6 is pressed down, which decreases the gap between state S5 and S6 , and then the NAC between them is strengthened. The changes in energy gap between state S5 and S6 can be seen in Fig. 4 (a) and (b). When an impurity is introduced into the polymer chain, the NAC terms that kept zero in case of pristine polymer chain are no longer zero, even take place great changes, such as σ54 , σ53 and σ32 , see the bottom row of Fig. 3. For example, in Fig. 3(b) NAC term σ54 kept zero all along, while in Fig. 3(f) NAC term σ54 shows many spikes at some moments in time evolution. At those moments, the NAC between state S5 and S4 is very strong, indicating that the system has very high probabilities of jumping between state S5 and S4 . The above

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results show that the restriction of jumping between EX-type and CT-type excited state is completely removed due to the introduction of impurity. We will see that these changes in NAC terms will result in great influence on the relaxation of excited states. Now we turn to discussing the dynamics of the potential energy surfaces from state S1 to S7 for a typical trajectory. In Fig. 4, we show the time evolution of potential energy surfaces from state S1 to S7 for the typical trajectory used in Fig. 2 and Fig. 3. Let’s first look at Fig. 4(a). It is for the pristine polymer, and the system remains on state S6 all along. In this plot, all curves display small oscillations which should be related to C-C bond stretching. We have known that state S6 , S5 , S3 and S1 are EX-type excited states. During the time evolution, the energies of state S6 and S5 are very close. This explains why NAC term σ65 is so strong as shown in panel A (b) of Fig. 2. Nevertheless, the energy gaps between state S5 and S3 , S3 and S1 are much bigger. This will lead to the difficulties of jumping from state S5 to S3 , as well as from state S3 and S1 . Considering the prohibition of transitions from state S5 to S4 and from state S3 to S2 , the lifetime of state S5 and S3 should be long. Fig. 4(b) is for the pristine polymer and the system evolves on state S5 . We find that the energy gap between state S6 and S5 in Fig. 4(b) is markedly larger than that in Fig. 4(a). At the same time, the energy gap between state S5 and S4 in Fig. 4(b) is markedly smaller than that in Fig. 4(a). This shows that if the system occupies an excited state the energy level of this excited state will be pressed down during evolution, narrowing the gap with it’s neighbor excited state. When the energy level of state S5 is approaching state S4 , we observe a lot of level crossings. These level crossings also can be observed between state S7 and S6 . They are the so-called “trivial crossings” in surface hopping simulations 32 . Here, we note that we observe “trivial crossings” because state S4 and S7 are CT-type excited states, which do not interact with EX-type excited state S5 and S6 , respectively 25 . In contrast, we didn’t observe “trivial crossings” between state S6 and S5 in Fig. 4(a) because they belong to the same type. Fig. 4(c) and (d) are for the impurity doped polymer chain. Compared with Fig. 4(a)

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-195.5 0

50

100

150

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energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 27

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(c)

0

100

150

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-191.0

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-191.5

-192.0

-192.0

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50

200

(d)

-195.5 0

50

100

150

200

0

50

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time (fs)

time (fs)

Figure 4: The time evolution of potential energy surfaces for a typical trajectory. The left column is for time evolution on state S6 , and the right column for time evolution on state S5 . The top row is for the pristine polymer chain, and the bottom row for impurity doped polymer chain with Vimp = −0.5 eV.

14


Page 15 of 27

and (b), the whole spectrum is lowered around 0.5 eV due to the introduction of impurity. In Fig. 4(d), we do not see any “trivial crossings” between S7 and S6 , as well as S5 and S4 . This is because the impurity makes the NAC between them no longer equal zero. In other words, they are no longer non-interacting excited states. 1.0

1.0

0.9

S

S

S

S

S

2

3

(a)

4

1.0

(b)

0.9

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6

S

(c)

0.9

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5

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S

1

0.8

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(d)

4

0

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(e)

0.9

(f)

0.9

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0.3

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6

S

population

7

0

500

1000

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3000

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0.0 0

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(g)

0.9 0.8

0

0.7

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0.4

0.3

0.3

0.3

0.2

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0.1

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0.0

S

S

S

S

S

1

0.6

3

0.5

5

0.4

2

2000

2500

3000

(i)

6

7

500

1500

4

S

0

1000

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500

1.0

(h)

0.9 0.8

0.7 population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1000

1500 time (fs)

2000

2500

3000

0.0 0

500

1000

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2500

time (fs)

3000

0

500

1000

1500

2000

2500

3000

time (fs)

Figure 5: Time dependence of the populations (i.e., the occupation probabilities) of the lowest seven singlet excited states, averaged over 400 trajectories. The left column corresponds for Vimp = 0, the middle column Vimp = -0.5 eV and the right column Vimp = -1.0 eV. In the following, we will discuss the relaxation of high-lying excited states S6 , S5 and S3 , 15



respectively, for the pristine and impurity doped polymers. Fig. 5 shows the time evolution of the populations of the lowest seven excited states, averaged over 400 trajectories. The left column of Fig. 5 is for the pristine polymer. In Fig. 5(a), the system is initially excited to state S6 . It almost immediately depopulates to state S5 . This is because of the strong coupling between state S6 and S5 , as shown in panel A (b) of Fig. 2. We do not observe upward transitions from state S6 to S7 . Then, state S3 and S1 are populated, and no hops from state S5 to S4 , and from state S3 to S2 are observed. These results are coincide with the results shown in panel A of Fig. 2, where NAC terms σ54 and σ32 remains zero throughout time evolution since they belong to different types. In Fig. 5(d), the system is initially excited to state S5 . In this case, the decay of state S5 is very slow compared with the decay of state S6 . This is because state S5 does not interact with state S4 , and has relatively weak coupling with S3 , as shown in the top row of Fig. 3. We can observe a small number of upward transitions from state S5 to S6 at the first stage of time evolution. This is obviously because of the strong coupling between state S5 and S6 . The middle column of Fig. 5 is for the impurity doped polymer chain with Vimp = -0.5 eV. We can see that the impurity has remarkable influence on the relaxation of excited states S6 , S5 and S3 . For example, let’s compare Fig. 5(d) and (e). In Fig. 5(e), the clear difference from Fig. 5(d) is that, besides state S3 and S1 , state S4 and S2 are populated. The reason is that the restriction of jumping between EX-type and CT-type excited state is removed due to the introduction of impurity, as we have discussed above. In addition to this, the decay of state S5 is much faster than the decay in the pristine polymer. The decay behavior of state S5 is approximately described by an exponential function nS5 = exp(−t/τS5 ). This gives the lifetime of state S5 1076 fs and 109 fs for Fig. 5(d) and (e), respectively. In other words, the impurity significantly reduces the lifetime of state S5 . In Fig. 5(e), the fast decay of state S5 comes from the strong NAC between state S5 and S4 at the moments with spikes [see Fig. 3(f)]. At these moments, the probabilities of jumping between state S5 and S4 are very high. This is also why we see a lot of high-frequency oscillations in the curves of state S5 and S4 .

16


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Not only in Fig. 5(e), in Fig. 5(b) and (h), the lifetimes of state S6 and S3 are also reduced by the impurity. If the impurity strength increases to -1.0 eV, see the right column of Fig. 5, we find the lifetimes of state S6 , S5 and S3 are further reduced.

Conclusions To summarize, we have investigated the impurity effects on excited-state dynamics of a single polymer chain by performing FSSH simulations. We first classify all excited states into two types: EX-type and CT-type, according to whether the diagonal elements of their transition density matrices being zero or not. For a pristine polymer chain, the system never jumps between EX-type excited state and CT-type excited state because the NAC terms between different types of excited states keep zero during evolution. If an impurity is introduced into the polymer chain, the restriction of jumping between different types of excited states will be removed. The results underline the broken electron-hole symmetry of excited-state wavefunctions due to the introduction of impurity. Through changing the strength of nonadiabatic couplings between excited states, the impurity has significant effects on the relaxation of high-lying excited states. It makes CT-type excited states involved in the excited-state dynamics process, and dramatically reduces the lifetime of initially excited state.

Acknowledgement This work was supported by Zhejiang Provincial Science Foundation of China (LY19A040007), Zhejiang Provincial Education Department General Research Project(KYZ04Y18250), National Natural Science Foundation of China (11574180), and Hebei Province Department of Education (GCC2014025).

17



References (1) Sekine, C.; Tsubata, Y.; Yamada, T.; Kitano, M.; Doi, S. Recent progress of high performance polymer OLED and OPV materials for organic printed electronics. Sci. Technol. Adv. Mater. 2014, 15, 034203. (2) Meng, R.; Li, Y.; Gao, K.; Qin, W.; Wang, L. Ultrafast exciton migration and dissociation in π-conjugated polymers driven by local nonuniform electric fields. J. Phys. Chem. C 2017, 121, 20546–20552. (3) Sun, Z.; Stafström, S. Spin-dependent polaron recombination in conjugated polymers. J. Chem. Phys. 2012, 136, 414–R. (4) Li, X.; Hou, D.; Chen, G. Effect of electron-electron interaction on scattering process of oppositely charged polarons in conjugated polymers. Organic Electronics 2018, 54, 245–254. (5) Zhen, S.; Desheng, L.; Sven, S.; Zhong, A. Scattering process between polaron and exciton in conjugated polymers. J. Chem. Phys. 2011, 134, 539–R. (6) An, Z.; Wu, C. Q.; Sun, X. Dynamics of photogenerated polarons in conjugated polymers. Phys. Rev. Lett. 2004, 93, 216407. (7) Miranda, R. P.; Fisher, A. J.; Stella, L.; Horsfield, A. P. A multiconfigurational timedependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states. J. Chem. Phys. 2011, 134, 244101. (8) Miranda, R. P.; Fisher, A. J.; Stella, L.; Horsfield, A. P. A multiconfigurational timedependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains. J. Chem. Phys. 2011, 134, 244102. (9) Doltsinis, N. L. Nonadiabatic dynamics: mean-field and surface hopping. Quantum

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simulations of complex many-body systems: from theory to algorithms 2002, 10, 377– 397. (10) Tully, J. C. Molecular dynamics with electronic transitions. J. Chem. Phys. 1990, 93, 1061–1071. (11) Wang, L.; Akimov, A.; Prezhdo, O. V. Recent progress in surface hopping: 2011–2015. J. Phys. Chem. Lett. 2016, 7, 2100–2112. (12) Crespo-Otero, R.; Barbatti, M. Recent advances and perspectives on nonadiabatic mixed quantum–classical dynamics. Chem. Rev. 2018, 118, 7026–7068. (13) Nelson, T.; Fernandezalberti, S.; Chernyak, V.; Roitberg, A. E.; Tretiak, S. Nonadiabatic excited-state molecular dynamics modeling of photoinduced dynamics in conjugated molecules. J. Phys. Chem. B 2011, 115, 5402–14. (14) Barbatti, M.; Crespo-Otero, R. Density-functional methods for excited states; Springer, 2014; pp 415–444. (15) Mitrić, R.; Werner, U.; Bonačićkoutecký, V. Nonadiabatic dynamics and simulation of time resolved photoelectron spectra within time-dependent density functional theory: Ultrafast photoswitching in benzylideneaniline. J. Chem. Phys. 2008, 129, 164118. (16) Sterpone, F.; Rossky, P. J. Molecular modeling and simulation of conjugated polymer oligomers: Ground and excited state chain dynamics of PPV in the gas phase. J. Phys. Chem. B 2008, 112, 4983–4993. (17) Sterpone, F.; Bedardhearn, M. J.; Rossky, P. J. Nonadiabatic mixed quantum-classical dynamic simulation of π-stacked oligophenylenevinylenes. J. Phys. Chem. A 2009, 113, 3427–30. (18) Bedard-Hearn, M. J.; Sterpone, F.; Rossky, P. J. Nonadiabatic simulations of exciton

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dissociation in poly-p-phenylenevinylene oligomers. J. Phys. Chem. A 2010, 114, 7661– 7670. (19) Nelson, T.; Fernandezalberti, S.; Roitberg, A. E.; Tretiak, S. Nonadiabatic excitedstate molecular dynamics: modeling photophysics in organic conjugated materials. Acc. Chem. Res. 2014, 47, 1155–64. (20) Fazzi, D.; Barbatti, M.; Thiel, W. Modeling ultrafast exciton deactivation in oligothiophenes via nonadiabatic dynamics. Phys. Chem. Chem. Phys. 2015, 17, 7787–99. (21) Köhler, A.; Dos Santos, D.; Beljonne, D.; Shuai, Z.; Brédas, J.-L.; Holmes, A.; Kraus, A.; Müllen, K.; Friend, R. Charge separation in localized and delocalized electronic states in polymeric semiconductors. Nature 1998, 392, 903–906. (22) Brédas, J.-L.; Cornil, J.; Beljonne, D.; Dos Santos, D. A.; Shuai, Z. Excited-state electronic structure of conjugated oligomers and polymers: a quantum-chemical approach to optical phenomena. Acc. Chem. Res. 1999, 32, 267–276. (23) Bittner, E. R.; Ramon, J. G. S.; Karabunarliev, S. Exciton dissociation dynamics in model donor-acceptor polymer heterojunctions. i. energetics and spectra. J. Chem. Phys. 2005, 122, 214719. (24) Zhen, S.; Sheng, L.; Xie, S.; Zhong, A. A study on excited-state properties of conjugated polymers using the Pariser-Parr-Pople-Peierls model combined with configurationinteraction-singles. Organic Electronics 2018, 57, 277–284. (25) Sun, Z.; Li, S.; Xie, S.; An, Z. Solution for the trivial crossing problem in surface hopping simulations by the classification on excited states. J. Phys. Chem. C 2018, 122, 8058–8064. (26) Jug, K. Theoretical basis and design of the PPP model Hamiltonian. Int. J. Quantum Chem. 1990, 37, 403–414. 20


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(27) Ribeiro, L. A.; da Cunha, W. F.; Neto, P. H. O.; Gargano, R.; e Silva, G. M. Impurity effects and temperature influence on the exciton dissociation dynamics in conjugated polymers. Chem. Phys. Lett. 2013, 580, 108–114. (28) Ribeiro, L. A.; da Cunha, W. F.; de Oliveira Neto, P. H.; Gargano, R.; e Silva, G. M. Dynamical study of impurity effects on bipolaron–bipolaron and bipolaron–polaron scattering in conjugated polymers. J. Phys. Chem. B 2013, 117, 11801–11811. (29) Chandross, M.; Mazumdar, S. Coulomb interactions and linear, nonlinear, and triplet absorption in poly (para-phenylenevinylene). Phys. Rev. B 1997, 55, 1497. (30) Paterlini, M. G.; Ferguson, D. M. Constant temperature simulations using the Langevin equation with velocity Verlet integration. Chem. Phys. 1998, 236, 243–252. (31) Tretiak, S.; Mukamel, S. Density matrix analysis and simulation of electronic excitations in conjugated and aggregated molecules. Chem. Rev. 2002, 102, 3171–3212. (32) Fernandezalberti, S.; Roitberg, A. E.; Nelson, T.; Tretiak, S. Identification of unavoided crossings in nonadiabatic photoexcited dynamics involving multiple electronic states in polyatomic conjugated molecules. J. Chem. Phys. 2012, 137, 460–19249.

21



List of Figures 1.0

1.0

0.9

S

S

S

S

S

S

1

0.8

population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 27

2

4

0.9

3

5

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S

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S

4

2

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7

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2000

time (fs)

time (fs)

TOC graph

22

3

S

0.7

0.6

S

1

0.8

6

S

S


2500

3000

site site site

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


site

Page 23 of 27

20 18 16 14 12 10 8 6 4 2 20 18 16 14 12 10 8 6 4 2 20 18 16 14 12 10 8 6 4 2 20 18 16 14 12 10 8 6 4 2

20 18 16 14 12 10 8 6 4 2

S 1

2 4 6 8 10 12 14 16 18 20 S 5

2 4 6 8 10 12 14 16 18 20 '

S 1

2 4 6 8 10 12 14 16 18 20 '

S 5

2 4 6 8 10 12 14 16 18 20 site

20 18 16 14 12 10 8 6 4 2 20 18 16 14 12 10 8 6 4 2 20 18 16 14 12 10 8 6 4 2

20 18 16 14 12 10 8 6 4 2

S 2

2 4 6 8 10 12 14 16 18 20 S 6

2 4 6 8 10 12 14 16 18 20 '

S 2

2 4 6 8 10 12 14 16 18 20 '

S 6

20 18 16 14 12 10 8 6 4 2 20 18 16 14 12 10 8 6 4 2 20 18 16 14 12 10 8 6 4 2

2 4 6 8 10 12 14 16 18 20

20 18 16 14 12 10 8 6 4 2

S 3

2 4 6 8 10 12 14 16 18 20 S 7

2 4 6 8 10 12 14 16 18 20 '

S 3

2 4 6 8 10 12 14 16 18 20 '

S 7

2 4 6 8 10 12 14 16 18 20

site

site

Figure 1

23


20 18 16 14 12 10 8 6 4 2 20 18 16 14 12 10 8 6 4 2 20 18 16 14 12 10 8 6 4 2

S 4

2 4 6 8 10 12 14 16 18 20 S 8

2 4 6 8 10 12 14 16 18 20 '

S 4

2 4 6 8 10 12 14 16 18 20 '

S 8

2 4 6 8 10 12 14 16 18 20 site


A 0.06

0.06


(a)

(c)

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Page 24 of 27

-0.06 0

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Figure 2 24


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Page 25 of 27

A 0.06

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-0.06 0

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Figure 3

25


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100 time (fs)

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-190.5

S S

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S

energy (eV)

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(b)

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4

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50

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Page 26 of 27

200

(c)

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150

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Figure 4

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Page 27 of 27

1.0

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0

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2500

3000

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Figure 5

27


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Impurity Effects on Excited-State Dynamics of Conjugated Polymers

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