Intramolecular Singlet Fission: Insights from Quantum Dynamical

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Spectroscopy and Photochemistry; General Theory

Intramolecular Singlet Fission: Insights from Quantum Dynamical Simulations S. Rajagopala Reddy, Pedro Brana Coto, and Michael Thoss J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b02674 • Publication Date (Web): 26 Sep 2018 Downloaded from http://pubs.acs.org on September 27, 2018

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The Journal of Physical Chemistry Letters

Intramolecular Singlet Fission: Insights from Quantum Dynamical Simulations

S. Rajagopala Reddy,

†Institute

∗,†,§

∗,‡,k

Pedro B. Coto,

and Michael Thoss

∗,¶

of Theoretical Physics and Interdisciplinary Center for Molecular Materials,

Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany

‡Institute

of Theoretical Physics, Friedrich-Alexander-University Erlangen-Nürnberg, Erlangen, Germany

¶Institute §Current

of Physics, Albert-Ludwigs University Freiburg, Freiburg, Germany

address: Department of Computational Sciences, Central University of Punjab, Mansa Road, Bathinda, Punjab 151001, India

kCurrent

address: Department of Physical and Analytical Chemistry, University of Oviedo, Oviedo, Spain

E-mail: [email protected]; [email protected]; [email protected]

1

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The Journal of Physical Chemistry Letters 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

Abstract We investigate the dynamics of intramolecular singlet ssion in a dimer consisting of two pentacene-based chromophores covalently bonded to a phenylene spacer using an approach that combines high-level ab initio multireference perturbation theory methods and quantum dynamical simulations. The results show that the population of the multiexcitonic state, corresponding to the rst step of singlet ssion, is facilitated by the existence of higher-lying doubly excited and charge transfer states that participate in a superexchange-like way. The important role played by high-frequency ring-breathing molecular vibrations in the process is also discussed.

Graphical TOC Entry

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The ShockleyQueisser eciency limit

1

imposes a restriction on the maximum perfor-

mance of single junction solar cells. Over the years, dierent strategies have been explored to circumvent this limit. One possibility is the use of materials for the energy conversion step exhibiting charge carrier multiplication,

2

which allows quantum eciencies larger than

100% per absorbed photon. It is within this context that singlet ssion (SF) received renewed interest.

4,5

3

has recently

SF is a photophysical process in which a chromophore in a sin-

glet electronic excited state (S1 ) shares its excitation energy with another chromophore that is in the ground state and both transform into a pair of triplet electronic excited states (T1 ). The nascent T1 states are coupled forming a singlet state [also called multiexciton (ME) state], so the process is spin-allowed.

6,7

plain SF, the direct and the mediated.

3

Two mechanisms have mainly been advocated to exIn the direct mechanism, the optically excited state

transforms into the ME state, which later dissociates into two (non-interacting) T1 states. In the mediated mechanism, mixing with high-lying charge transfer (CT) states permits the population of the ME state from the optically excited state. Since ionization of the T1 states can provide two charge carriers, both mechanisms can potentially lead to the fabrication of highly-ecient SF-based solar cells and initial steps toward this goal have already been taken.

8,9

Motivated by these technological prospects, the last years have seen important theoretical research eorts devoted to understanding the mechanism of SF at the molecular level. This involves identifying the electronic states participating in the process, their specic roles and coupling mechanisms

3,2226

1021

as well as characterizing the dynamics of SF, unraveling the

role of coherence, interference, and coupling to molecular vibrations.

3,7,14,21,2531

These works

have identied key electronic and structural parameters that control the eciency of the process, a rst step in the development of ecient SF-based devices.

3,6,29,3239

While most of

these works have focused on the investigation of intermolecular SF in organic crystals and lms, it has recently become apparent that solutions of covalently linked bichromophoric systems bonded via organic bridges can also undergo SF.

3

4047


This process of intramolecular


Page 4 of 23

SF (iSF) not only opens the way to solution-processable SF-based photovoltaic devices

48

but

also provides perhaps the best scenario for understanding the mechanism of SF at a molecular level.

In this context, a series of 6,13-bis(triisopropylsilylethynyl)pentacene-derived

(TIPSP) dimers, where the pentacene-like moieties are covalently bonded to a phenylene spacer in ortho-, meta-, and para-conformations have recently been investigated by some of the authors.

43

These molecules were designed to impose geometrical restraints and hence

control the through-space and through-bond couplings between the electronic states involved in iSF.

43

Using time resolved spectroscopic techniques and high level ab initio methods, it

was shown that mixing between the optically excited state and CT states might be helpful to overcome the activation barrier of SF. Although these results provided insight into the roles of the dierent excited electronic states involved, the inuence of electronic-vibrational coupling, which may be instrumental for ecient SF,

49,50

was not addressed.

In this Letter, we address this aspect and investigate the dynamics of iSF for a simplied model of o-TIPSP, where the triisopropylsilyl groups have been modeled using methyl groups (o-TIPSPm, see Fig. 1). The motivation for the investigation of this particular regioisomer is four-fold. First, this study sheds light on the timescale of SF in this system, an information that could not be obtained in detail from experiment for this system. Second, o-TIPSP has a well dened structure that incorporates both through-space and through-bond couplings and the characterization of the dynamics of SF provides information on vibrational eects on these couplings.

Third, CT states appear relatively low in energy in o-TIPSP, which

allows to ascertain if a signicant population of these states promoted by vibronic coupling is possible. Finally, this study provides detailed information on the relative contributions of the direct and mediated channels to SF. For the simulation of the dynamics of iSF in o-TIPSP we have used high-level ab initio multireference perturbation theory methods to build the potential energy surfaces of the dierent states and the quantum dynamical calculations were carried out using the multilayer multiconguration time-dependent Hatree (ML-MCTDH) method.

4


5158

Specically, we solve

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Figure 1: o-Bis(13-(methylethynyl)pentacen-6-yl)ethynyl)benzene dimer (o-TIPSPm) investigated in this work.

the time-dependent Schrödinger equation using a vibronic coupling model Hamiltonian represented in a basis of diabatic states relevant for the process (see below).

59

This model

assumes that the initial state is prepared by an instantaneous excitation to the bright state (i.e. consistent with an experiment where an ultrashort femtosecond laser pulse is used). In the diabatic basis, the Hamiltonian reads (h ¯

H=

X

HI |IihI| +

I

where

I

and

J

= 1)

X

(VI,J |IihJ| + h.c.),

(1)

I>J

label the dierent diabatic electronic states. In this expression, the diagonal

and o-diagonal terms take the form

HI = EI0 +

X ωl l

2

(Q2l + Pl2 ) +

X l

5

1 l 2 (κlI,I Ql + γI,I Ql ) 2


(2)


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and

0 VI,J = VI,J +

X l

Thereby,

0 EI0 and VI,J

1 l Q2l ). (κlI,J Ql + γI,J 2

(3)

are the diagonal and o-diagonal elements of the electronic Hamiltonian

(Hel ), i.e., the energies and electronic couplings of the diabatic electronic states considered in the model calculated at the ground state reference geometry.

Ql

and

Pl

are the (dimen-

sionless) coordinates and momenta of the vibrational degrees of freedom, represented by the normal modes in the electronic ground state of o-TIPSm.

The term

ωl 2 l 2 (Ql

P

+ Pl2 )

describes the kinetic and potential energy corresponding to these vibrational normal modes within the harmonic approximation. The other terms account for the rst and second order vibronic couplings, with

κlI,J

and

l γI,J

being the linear and quadratic coupling constants for

mode l , respectively. In the calculations reported below, 28 vibrational were included, which were selected based on the value of their respective dimensionless coupling strengths ( see Supporting Information).

κ2 , 2ω 2

59

Based on the model Hamiltonian, Eq. (1), we consider dierent observables to analyze distinct aspects of the SF process. The electronic dynamics is described by the time-dependent population of the dierent states involved in the process, given by

PL (t) = Tr {PL ρ(t)} ,

where

PL = |LihL|

e−iHt ρ(0)eiHt

(4)

is the projector onto the diabatic electronic state

is the density matrix at time

t.

|Ii

and

ρ(t) =

The initial density matrix is given by

ρ(0) = |Ii |00 ih00 | hI| ,

where

|Li

is the initially excited electronic states and

(5)

|00 i

is the vibrational ground state

in the electronic ground state of o-TIPSm (see Supporting Information). Thereby, we have

6


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assumed an ultrafast (instanteneous) excitation of the optically bright state temperature eects in the initial state.

|Li and neglected

In addition, the autocorrelation function of the

inititally excited state is considered,

C(t) = h00 | hI| e−iHt |Ii |00 i ,

(6)

the Fourier transform of which provides the photoabsorption cross-section. The parameters of the vibronic Hamiltonian, including the diabatic electronic states, energies and coupling constants, were obtained from the corresponding adiabatic electronic states using the diabatization method of Nakamura and Truhlar.

60,61

The adiabatic electronic

states were calculated using the extended multicongurational quasidegenerate perturbation theory method (XMCQDPT),

62

a double-ζ (DZV) basis set

63

and employing an eight roots-

equal weights state average complete active space self-consistent eld (CASSCF) calculation as reference. An active space of four electrons in four orbitals (HOMO and LUMO of each pentacene-like moiety) was used (see Supporting Information for further details). Table 1 contains the adiabatic vertical excitation energy, modulus of the dipole moment, oscillator strength and character of the lowest lying singlet excited states of o-TIPSPm calculated at the ground state equilibrium geometry. The four lowest-lying singlet excited states exhibit ME (S1 ), locally excited (LE)-like (S2 and S3 ), and CT (S4 ) character. These states lie in a close range of energy (∼0.2 eV, see Table 1), with S2 and S3 being quasidegenerate.

In addition, S4 is also near degenerate with S5 , a doubly excited (DE) state.

As a result of the small energy dierences, there is a signicant degree of mixing of the CT state with the rest of states, in particular with the LE and ME states. Finally, the last two states S6 and S7 of DE and CT character, respectively, are quasidegenerate and lie

∼0.2

eV

above S5 . We have used these adiabatic states to build the diabatic basis employed for the simulation of the dynamics of iSF. This basis comprises the electronic ground state

7


|1 (S0 S0 )i,

the LE


Page 8 of 23

Table 1: Adiabatic vertical excitation energy (∆E, in eV),a modulus of the dipole moment (µ, in D),b oscillator strength (f )b and character (char.)c of the lowestlying singlet excited states of o-TIPSPm calculated at the ground state equilibrium structure. State

∆E

S1

1.51 1.75 1.78 1.98 2.00 2.20 2.25

S2 S3 S4 S5 S6 S7

µ

f

char.

2.04

Intramolecular Singlet Fission: Insights from Quantum Dynamical

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