Ultrafast excited state relaxation in long-chain polyenes

Abstract

We present a comprehensive study, by femtosecond pump–probe spectroscopy, of excited state dynamics in a polyene that approaches the infinite chain limit. By excitation with sub-10-fs pulses resonant with the 0–0 S₀ → S₂ transition, we observe rapid loss of stimulated emission from the bright excited state S₂, followed by population of the hot S₁ state within 150 fs. Vibrational cooling of S₁ takes place within 500 fs and is followed by decay back to S₀ with 1 ps time constant. By excitation with excess vibrational energy we also observe the ultrafast formation of a long-living absorption, that is assigned to the triplet state generated by singlet fission.

Introduction

The electronic properties of polyenes, linear chains of π-conjugated carbon atoms, are under extensive investigation since the 1950s. There are several reasons for this interest:

• They are simple systems suitable for detailed experimental and theoretical characterization, so that they are considered as test banks for advanced quantum chemical methods [1];

• They are model compounds for the class of conjugated polymers, which are the focus of intense fundamental research due to their important technological impact [2];

• They are model compound for the class of carotenoids, sharing with them the backbone of alternating single and double carbon bonds [3]. Carotenoids perform a number of functions in photosynthetic systems [4], among which the most important are photoprotection and light harvesting. The molecular mechanisms of such processes are ultimately determined by the energies and lifetimes of their low-lying excited electronic states.

The simplest approach to describe a linear conjugated chain, based on the observation that π-electrons have p orbitals overlapping along the backbone, is the free-electron model, that describes the electron as a one-dimensional “particle in a box”. This model properly predicts that the optical (HOMO–LUMO) band-gap shifts to lower energies for increasing conjugation length n (number of conjugated double bonds in the chain). However, it also predicts that linear chains are emitting (since the lowest energy electronic excited state is “bright”, i.e. optically allowed) and become metallic (i.e. with zero gap) for infinite chain length. Both assertions turn out to be wrong, particularly the second one which contrasts with the Peierls theorem [5]. An efficient correction is provided by the model suggested by Kuhn [6], which phenomenologically introduced a modulation of the potential in order to describe alternation in the bond lengths along the chain, leading to a chain-length dependence of the energy levels of the type = A + B/n. The predicted saturation of band-gap for the infinite chain limit is indeed observed experimentally. Yet the model again fails in predicting the correct ordering of the excited states, and consequently their ability to reemit light. It turns out that simple one-electron models cannot account for the photophysics of linear chains, but both electron correlation and electron–phonon coupling must be included. A well-known model, proposed in 1979 and including only electron–phonon interaction, predicted the existence of exotic excited states in long chains, named solitons (for a review see [7]). While the latter have never been definitively confirmed experimentally, this prediction certainly fostered a huge research activity. Inclusion of electron correlation not only allows to correctly predict the chain-length dependence of the energy levels, but also explains the lack of emission in many polyenes and carotenoids.

According to the C_2h point group symmetry, the first allowed optical transition in polyenes occurs from an 1${}^1{\text{A}}_{\text{g}}^{-}$ state (the ground state S₀) to a ${\text{B}}_{\text{u}}^{+}$ state. However, for all polyenes with n > 3, there is an additional “covalent” excited state of ${\text{A}}_{\text{g}}^{-}$ symmetry with energy lower than the ${\text{B}}_{\text{u}}^{+}$ state [8], [9]. For this reason, the bright $1^1{\text{B}}_{\text{u}}^{+}$ state is called S₂, while the lower energy dark $2^1{\text{A}}_{\text{g}}^{-}$ state is known as S₁. The dark state acts as a sink for the excitation energy, so that the excited state dynamics of polyenes is characterized by very rapid energy relaxation processes. Following photoexcitation, deactivation of S₂ to S₁ occurs via an Internal Conversion (IC) process on the timescale of a few hundreds of femtoseconds [10], [11], [12]; S₁ then decays back to the ground state S₀ through another, slower, IC process, on the picosecond timescale [13].

An open issue of the photophysics of linear conjugated chains is understanding the chain-length dependence of the IC rates. The energy gap law for radiationless transitions in large molecules [14] predicts a transition rate k ÷ exp(−βΔE), where ΔE is the energy gap between the levels. According to this law, the IC rate should decrease with increasing energy gap between the converting levels. The gap law describes quite well the S₁ → S₀ relaxation, since the S₀–S₁ gap shrinks for increasing conjugation length, leading to an increase of the IC rate, as experimentally observed [13]. Such simple description, however, fails for the S₂ → S₁ relaxation process. Both theoretical and experimental results indicate that the S₁–S₂ gap increases with n, so that the IC rate, according to the gap law, is expected to decrease for increasing conjugation length. However, experiments using both fluorescence up-conversion [15] and transient absorption [16] showed a different behaviour. The S₂ lifetime was found to increase with n for short carotenoids (5 ⩽ n ⩽ 9), in accordance with the energy gap law; for n > 9, on the other hand, it was found to decrease with conjugation length. To explain this peculiar chain-length dependence the presence of additional excited singlet states besides the $1^1{\text{B}}_{\text{u}}^{+}$ has been invoked; such states (more specifically the $1^1{\text{B}}_{\text{u}}^{-}$ and $3^1{\text{A}}_{\text{g}}^{-}$ states) have been predicted theoretically [17], [1]. It has been proposed that, for carotenoids with conjugation length n > 9, their energy lies within the S₁–S₂ gap and thus they become active, as intermediate states, in the S₂ → S₁ IC process. However, their direct experimental observation is still controversial [18].

In addition to IC, another possible deactivation pathway for S₂ and S₁ is intersystem crossing (ISC) to the triplet manifold. In naturally occurring polyenes excited triplet states play a key role in vital photoprotection processes, by scavenging triplet excited states in (bacterio)chlorophylls and singlet oxygen. Only limited experimental data are available on the energy of triplet states in polyenes [19], due to an extremely low phosphorescence quantum yield, of the order of 10⁻⁴–10⁻⁵. ISC through the usual spin-flip mechanism is expected to display a very low quantum yield, since the singlet excited state lifetime of carotenoids is very short. An alternative ISC pathway is singlet fission, i.e. spontaneous breaking of a singlet into two triplet states. Such process has been recently observed in carotenoids bound to BChls in antenna complexes [20], [21] and in long polydyacetylene chains [22].

The study of conjugation length dependence of the photophysics of polyenes has been both a tool and an object for research. Changing the conjugation length provides a set of data for better matching with theory, and it also shows how the system evolves from a molecular-like behaviour to the limit of a one-dimensional quantum confined solid. So far, however, spectroscopic studies on polyenes have been limited to molecules with no more than fifteen double bonds, essentially because of the lack of suitable synthesis methods. Some extrapolations from short-chain models have been used to predict properties and behaviour of the longest polyene compounds, but they have not been matched by a corresponding amount of experimental work.

In this work, we aim at filling this gap by studying a polyene that approaches the infinite chain limit, poly-diethyldipropargylmalonate, poly(DEDPM) [23]. Previous investigations showed that a poly(DEDPM) solution contains a distribution of conjugation lengths, mainly dominated by the longer segments with a number of conjugated double bonds greater than 100. This system is ideal for studying the excited state dynamics of polyenes for the limiting case of infinite chain length. First this allows us to study the IC process in very long chains, and second it allows us to explore what happens in long chains when excess energy is provided to the excited states, possibly highlighting quasi-particles dynamics. In particular we want to verify the possibility that, for high n values, bound covalent states can undergo fission into triplet pairs, as predicted by theory [1].