arXiv subjects

William Barford

Publications and source records attributed to William Barford.

At least 19 recordsLinked to original sources

arXiv2026

Triplet-Pair Character of the $2^1A_g$ Dark State of Polyenes

We define and calculate the triplet-pair population of the $2^1A_g$ dark state in polyenes, as predicted by the $\pi$-electron Pariser-Parr-Pople (PPP) model, for chains of 8 to 14 C-atoms and Coulomb interaction parameter between 4-14 eV. Our definition of the triplet-pair population is motivated by a two-particle model of the $2^1A_g$ state. We use DMRG to solve the PPP model and we exploit the MPS representation of the DMRG wavefunction to compute the triplet-pair population. Using our results for short chain sizes, we predict a finite-size scaling value of the triplet-pair population of ca. 75% for realistic Coulomb interactions for polyene chains. Our results agree with other theoretical work on the doubly-excited character of polyenes, and represents further evidence that the $2^1A_g$ state is predominantly triplet-pair in character - with implications for singlet fission mechanisms in polyenes.

physics.chem-ph↗

arXiv2025

Temperature Dependence of Charge and Exciton Transport in One-Dimensional Systems Subject to Static and Dynamic Disorder

The temperature-dependence of dynamical properties (e.g., the asymptotic diffusion coefficient and the sub-diffusive exponent) are calculated for charges and excitons in one-dimensional systems subject to static and dynamic disorder. These properties are determined by three complementary methods. One approach is via the time-integration of the velocity autocorrelation function. The second is via the mean-squared-displacement of thermal wavepackets subject to stochastic collapse via Lindblad jump operators. These two methods are applicable in the high-temperature regime, where the noise is temporally uncorrelated. In this regime the noise causes particle localization and the transport is diffusive. The third approach -- applicable in the low-temperature regime -- is weak-coupling Redfield theory. Here, static disorder causes particle localization. When the dynamics is diffusive, the diffusion coefficient is a non-monotonic function of temperature, increasing with temperature in the low-temperature Environment Assisted Quantum Transport regime and decreasing with temperature in the high-temperature quantum-Zeno regime. For any temperature, static and dynamic disorder decreases the diffusion coefficient. The dynamics is non-diffusive for thermal energies deep within the manifold of local-ground-states, where the sub-diffusive exponent decreases with increasing disorder and decreasing temperature.

physics.chem-ph↗

arXiv2025

A Vibronic Coupling Model to Study the Nonadiabatic Dynamics of Polyenes

We develop a linear vibronic coupling (LVC) model for polyenes described by the extended Hubbard-Peierls Hamiltonian. This model is applied to trans-hexatriene to benchmark quantum-classical dynamics methods against fully quantum simulations. We find that surface-hopping methods describe short times more accurately than multi-trajectory Ehrenfest. None of the quantum-classical methods studied obtain the long-time population oscillations found in fully quantum simulations. Varying the parameters of the LVC Hamiltonian, we find that surface hopping reproduces the correct trends in the long-time dynamics across a wide range of parameters, but generally overestimates the degree of internal conversion. On the other hand, multi-trajectory Ehrenfest gives more accurate long-time populations in proximity to the hexatriene parameter set.

physics.chem-ph↗

arXiv2024

Singlet Fission in Carotenoid Dimers -- The Role of the Exchange and Dipolar Interactions

A theory of singlet fission in carotenoid dimers is presented which aims to explain the mechanism behind the creation of two uncorrelated triplets. Following the initial photoexcitation of a carotenoid chain to a "bright" $n^1B_u^+$ state, there is ultrafast internal conversion to the intrachain "dark" $1^1B_u^-$ triplet-pair state. This strongly exchanged-coupled state evolves into a pair of triplets on separate chains and spin-decoheres to form a pair of single, unentangled triplets, corresponding to complete singlet fission. The simulated EPR spectra for lycopene dimers shows a distinct spectral signal due to the residual exchange coupling between the triplet-pairs on seperate carotenoid chains.

physics.chem-ph↗

arXiv2024

Using the Haken-Strobl-Reineker Model to Determine the Temperature Dependence of the Diffusion Coefficient

Stochastic quantum Liouville equations (SQLE) are widely used to model energy and charge dynamics in molecular systems. The Haken-Strobl-Reineker (HSR) SQLE is a particular paradigm in which the dynamical noise that destroys quantum coherences arises from a white noise (i.e., constant-frequency) spectrum. A system subject to the HSR SQLE thus evolves to its `high-temperature' limit, whereby all the eigenstates are equally populated. This result would seem to imply that the predictions of the HSR model, e.g., the temperature dependence of the diffusion coefficient, have no validity for temperatures lower than the particle bandwidth. The purpose of this paper is to show that this assumption is incorrect for translationally invariant systems. In particular, provided that the diffusion coefficient is determined via the mean-squared-displacement, considerations about detailed-balance are irrelevant. Consequently, the high-temperature prediction for the temperature dependence of the diffusion coefficient may be extrapolated to lower temperatures, provided that the bath remains classical. Thus, for diagonal dynamical disorder the long-time diffusion coefficient, $D_{\infty}(T) = c_{1} /T$, while for both diagonal and off-diagonal disorder, $D_{\infty}(T) = c_{1}/T + c_{2} T$, where $c_{2} \ll c_{1}$. An appendix discusses an alternative interpretation from the HSR model of the `quantum to classical' dynamics transition, whereby the dynamics is described as stochastically punctuated coherent motion.

physics.chem-ph↗

arXiv2023

Singlet Fission in Lycopene H-Aggregates

A theory of singlet fission (SF) in carotenoid dimers is applied to explain the SF in lycopene H-aggregates observed after high energy photoexcitation. The explanation proposed here is that a high energy, delocalized bright $^1B_u^+$ state first relaxes and localizes onto a single lycopene monomer. The high-energy intramonomer state then undergoes internal conversion to the $1^1B_u^-$ state. Once populated, the $1^1B_u^-$ state allows exothermic bimolecular singlet fission, while its internal conversion to the $2^1A_g^-$ state is symmetry forbidden. The simulation of SF predicts that the intramonomer triplet-pair state undergoes complete population transfer to the intermonomer singlet triplet-pair state within 100 ps. ZFS interactions then begin to partially populate the intermonomer quintet triplet-pair state up to ca. 2 ns, after which hyperfine interactions thermally equilibrate the triplet-pair states, thus forming free, single triplets within ca. 0.1 $μ$s.

physics.chem-ph↗

arXiv2023

Theory of Singlet Fission in Carotenoid Dimers

We develop a theory of singlet fission in carotenoid dimers. Following photoexcitation of the 'bright' state (i.e., a singlet electron-hole pair) in a single carotenoid, the first step in the singlet fission process is ultrafast intramolecular conversion into the highly-correlated 'dark' (or 2Ag) state. This state has both entangled singlet triplet-pair and charge-transfer character. Our theory is predicated on the assumption that it is the singlet triplet-pair component of the 'dark' state that undergoes bimolecular singlet fission. We use valence bond theory to develop a minimal two-chain model of the triplet-pair states. The single and double chain triplet-pair spectrum is described, as this helps explain the dynamics and the equilibrated populations. We simulate the dynamics of the initial entangled pair state using the quantum Liouville equation, including both spin-conserving and spin-nonconserving dephasing processes. By computing the intrachain and interchain singlet, triplet and quintet triplet-pair populations, we show that singlet fission depends critically on the interchain coupling and the driving potential (that determines endothermic versus exothermic fission). We also show that the Horodecki pair-entanglement provides a good metric for singlet fission.

physics.chem-ph↗

arXiv2022

Photoexcited state dynamics and singlet fission in carotenoids

We describe our dynamical simulations of the excited states of the carotenoid, neurosporene, following its photoexcitation into the 'bright' (nominally $1^1B_u^+$) state. We employ the adaptive tDMRG method on the UV model of $π$-conjugated electrons and use the Ehrenfest equations of motion to simulate the coupled nuclei dynamics. To account for the experimental and theoretical uncertainty in the relative energetic ordering of the nominal $1^1B_u^+$ and $2^1A_g^-$ states at the Franck-Condon point, we consider two parameter sets. In both cases there is ultrafast internal conversion from the 'bright' state to a 'dark' singlet triplet-pair state. We make a direct connection from our predictions to experimental observables by calculating the transient absorption. For the case of direct $1^1B_u^+$ to $2^1A_g^-$ internal conversion, we show that the dominant transition at ca. 2 eV, being close to but lower in energy than the $T_1$ to $T_1^*$ transition, can be attributed to the $2^1A_g^-$ component of $S_1$. Moreover, we show that it is the charge-transfer exciton component of the $2^1A_g^-$ state that is responsible for this transition, and not its triplet-pair component. We next discuss the microscopic mechanism of 'bright' to 'dark' state internal conversion, emphasising that this occurs via the exciton components of both states. Finally, we describe a mechanism whereby the strongly bound intrachain triplet-pairs of the 'dark' state may undergo interchain exothermic dissociation. We predict that this is only possible if the molecules are twisted in their ground states. The computational methodology underlying the calculations described here is explained in our companion paper, $\textit{Dynamical simulations of carotenoid photoexcited states using density matrix renormalization group techniques}$, D. Manawadu, D. J. Valentine, and W. Barford, $\textit{J. Chem. Theo. Comp.}$ (2023).

physics.chem-ph↗

arXiv2022

Dynamical simulations of carotenoid photoexcited states using density matrix renormalization group techniques

We present a dynamical simulation scheme to model the highly correlated excited state dynamics of linear polyenes. We apply it to investigate the internal conversion processes of carotenoids following their photoexcitation. We use the extended Hubbard-Peierls model, $\hat{H}_{\textrm{UVP}}$, to describe the $π$-electronic system coupled to nuclear degrees of freedom supplemented by a Hamiltonian, $\hat{H}_ε$, that explicitly breaks both the particle-hole and two-fold rotation symmetries of idealized carotenoids. The electronic degrees of freedom are treated quantum mechanically by solving the time-dependent Schrödinger equation using the adaptive time-dependent DMRG (tDMRG) method, while nuclear dynamics are treated via the Ehrenfest equations of motion. By defining adiabatic excited states as the eigenstates of the full Hamiltonian, $\hat{H}=\hat{H}_{\textrm{UVP}}+\hat{H}_ε$, and diabatic excited states as eigenstates of $\hat{H}_{\textrm{UVP}}$, we present a computational framework to monitor the internal conversion process from the initial photoexcited state to the singlet triplet-pair states of carotenoids. We further incorporate Lanczos-DMRG to the tDMRG-Ehrenfest method to calculate transient absorption spectra from the evolving photoexcited state. We describe the accuracy and convergence criteria for DMRG, and show that this method accurately describes the dynamics of carotenoid excited states. We also discuss the effect of $\hat{H}_ε$ on the internal conversion process, and show that its effect on the extent of internal conversion can be described by a Landau-Zener-type transition. This methodological paper is a companion to our more explanatory discussion of carotenoid excited state dynamics in, $\textit{Photoexcited state dynamics and singlet fission in carotenoids}$, D. Manawadu, T. N. Georges and W. Barford, $\textit{J. Phys. Chem. A}$ (2023).

physics.chem-ph↗

arXiv2022

Theory of the Dark State of Polyenes and Carotenoids

A theory is developed to describe the singlet dark state (usually labeled S1 or 2Ag) of polyenes and carotenoids. The theory assumes that in principle this state is a linear combination of a singlet triplet-pair and an odd-parity charge-transfer exciton. Crucially, these components only couple when the triplet-pair occupies neighboring dimers, such that an electron transfer between the triplets creates a nearest-neighbor charge-transfer excitation. This local coupling stabilises the 2Ag state and induces a nearest neighbor attraction between the triplets. In addition, because of the electron-hole attraction in the exciton, the increased probability that the electron-hole pair occupies neighboring dimers enhances the triplet-triplet attraction: the triplet pair is `slaved' to the charge-transfer exciton. The theory also predicts that as the Coulomb interaction is increased, the 2Ag state evolves from a predominately odd-parity charge-transfer exciton state with a small component of triplet-pair character to a state predominately composed of a triplet-pair with some exciton character. Above a critical Coulomb interaction there is a decoupling of the triplet-pair and charge-transfer exciton subspaces, such that the 2Ag state becomes entirely composed of an unbound spin-correlated triplet pair. The predictions of this theory are qualitatively consistent with high-level density matrix renormalization group calculations of the Pariser-Parr-Pople (or extended Hubbard) model.

physics.chem-ph↗

arXiv2022

Thermally Driven Polaron Transport in Conjugated Polymers

We present a hybrid quantum-classical simulation of charge-polaron transport in conjugated polymers. The charge, which couples to the angular rotations of the monomers, is modeled via the time-dependent Schrödinger equation, while the monomers are treated classically via the Ehrenfest equations of motion. In addition, the system is thermalized by assuming that the monomers are subject to Brownian fluctuations modeled by the Langevin equation. Charge coupling to the monomer rotations localizes the particle into a Landau polaron, while the thermal fluctuations of the monomers causes polaron dynamics. The emergent low-energy scale of the model is the polaron reorganization energy, $E_r$, and thus $T_r = E_r/k_B$ is a convenient scale for the low-temperature dynamics. We investigate two types of dynamics -- both relevant for temperatures $T < T_r$. In the lower temperature regime the system remains in the same quasidiabatic state, corresponding to activationless polaron diffusion as the polaron crawls stochastically along the chain. As the temperature is raised, however, there is a cross-over to an additional activated transfer process which corresponds to hopping between diabatic states. We show that these processes exhibit Landau-Zener type dynamics. We note that as our model is general, it equally applies to exciton-polaron (i.e., energy) transport in conjugated polymers, and to charge and exciton polaron transport in quasi one-dimensional molecular stacks.

cond-mat.stat-mech↗

arXiv2021

Measuring Time-Dependent Induced Quantum Coherences via Two-Dimensional Coherence Spectroscopy

We propose a two-dimensional spectroscopic protocol for measuring the time-dependent coherences between the stationary states of a system induced by a time-dependent system-bath interaction. We also investigate the role of temporally-correlated noise on coherence dephasing. This protocol enables dynamical information about the system and its coupling to the environment to be determined. Our results are based on the quantum-trajectory method, and are obtained from both approximate, analytical and exact, numerical solutions of the time-dependent Schroedinger equation. As an example, we show how this protocol can be used to investigate exciton dynameds in conjugated polymers induced by the coupling of their torsional modes with the environment.

physics.chem-ph↗

arXiv2021

Singlet Triplet-Pair Production and Possible Singlet-Fission in Carotenoids

Internal conversion from the photoexcited state to a correlated singlet triplet-pair state is believed to be the precursor of singlet fission in carotenoids. We present numerical simulations of this process using a pi-electron model that fully accounts for electron-electron interactions and electron-nuclear coupling. The time-evolution of the electrons is determined rigorously using the time-dependent density matrix renormalization method, while the nuclei are evolved via the Ehrenfest equations of motion. We apply this to zeaxanthin, a carotenoid chain with 22 conjugated carbon atoms (i.e., 11 double bonds). We show that the internal conversion of the photoexcited state to the singlet triplet-pair state occurs adiabatically via an avoided crossing within 100 fs and we predict a yield of ~ 50% We further discuss whether this singlet triplet-pair state will undergo exothermic versus endothermic intra or inter chain singlet fission.

physics.chem-ph↗

arXiv2021

Ultrafast Fluorescence Depolarization in Conjugated Polymers

We report on large-scale simulations of intrachain exciton dynamics in poly(para-phenylene vinylene). Our coarse-grained model describes Frenkel exciton coupling to both fast, quantized C-C bond vibrations and slow, classical torsional modes. We also incorporate system-bath interactions. The dynamics are simulated using the Time Evolution Block Decimation method, which avoids the failures of the Ehrenfest approximation to describe decoherence processes and nonadiabatic interstate conversion. System-bath interactions are modeled using quantum trajectories and Lindblad quantum jump operators. We find that following photoexcitation, the quantum mechanical entanglement of the exciton and C-C bond phonons causes exciton-site decoherence. Next, system-bath interactions cause the stochastic collapse of high-energy delocalized excitons onto chromophores. Finally, torsional relaxation causes additional exciton-density localization. We relate these dynamical processes to the predicted fluorescence depolarization and extract the timescales corresponding to them.

physics.chem-ph↗

arXiv2021

Exciton Dynamics in Conjugated Polymers

This is a review of exciton dynamics in conjugated polymers. Exciton dynamics encompass multiple time and length scales. Ultrafast femtosecond processes are intrachain and involve a quantum mechanical correlation of the exciton and nuclear degrees of freedom. In contrast, post-picosecond processes involve the incoherent Forster transfer of excitons between polymer chains. Exciton dynamics is also strongly determined by the spatial and temporal disorder that is ubiquitous in conjugated polymers. Since excitons are delocalized over hundreds of atoms, a theoretical understanding of these processes is only realistically possible by employing suitably parametrized coarse-grained exciton-phonon models. Moreover, to correctly account for ultrafast processes, the exciton and phonon modes must be treated on the same quantum mechanical basis and the Ehrenfest approximation must be abandoned. This further implies that sophisticated numerical techniques must be employed to solve these models. We begin by describing the energetic and spatial distribution of excitons in disordered polymer systems. Next, we discuss ultrafast intrachain exciton decoherence caused by exciton-phonon entanglement, which leads to fluorescence depolarization on the timescale of 10-fs. Interactions of the polymer with its environment causes the stochastic relaxation and localization of high-energy delocalized excitons onto chromophores. The coupling of excitons with torsional modes also leads to various dynamical processes. On sub-ps timescales it causes exciton density localization and local polymer planarization, while on post-ps timescales stochastic torsional fluctuations cause exciton diffusion along the polymer chain. Finally, we describe a first-principles, Forster-type model of intrachain exciton transfer and diffusion, whose starting point is a realistic description of the donor and acceptor chromophores.

physics.chem-ph↗

arXiv2020

Higher energy triplet-pair states in polyenes and their role in intramolecular singlet fission

Probing extended polyene systems with energy in excess of the bright state ($1^1B_u^+$/$S_2$) band edge generates triplets via singlet fission. This process is not thought to involve the $2^1A_g^-$/$S_1$ state, suggesting that other states play a role. Using density matrix renormalisation group (DMRG) calculations of the Pariser-Parr-Pople-Peierls Hamiltonian, we investigate candidate states that could be involved in singlet fission. We find that the relaxed $1^1B_u^-$, and $3^1A_g^-$ singlet states and $1^5A_g^-$ quintet state lie below the $S_2$ state. The $1^1B_u^-$, $3^1A_g^-$ and $1^5A_g^-$ states are all thought to have triplet-triplet character, which is confirmed by our calculations of bond dimerization, spin-spin correlation and wavefunction overlap with products of triplet states. We thus show that there is a family of singlet excitations(i.e., $2^1A_g^-$, $1^1B_u^-$, $3^1A_g^-$, $\cdots$), composed of both triplet-pair and electron-hole character, which are fundamentally the same excitation, but have different center-of-mass energies. The lowest energy member of this family, the $2^1A_g^-$ state, cannot undergo singlet fission. But higher energy members (e.g., the $3^1A_g^-$) state, owing to their increased kinetic energy and reduced electron-lattice relaxation, can undergo singlet fission for certain chain lengths.

cond-mat.str-el↗

arXiv2020

Triplet-Triplet Decoherence in Singlet Fission

Singlet fission is commonly defined to involve a process by which an overall singlet state with local triplet structure spin-decoheres into two triplet states, thereby completing the fission process. This process, often defined in loose terms involving the multiplicity of the overall state, is investigated here using a uniform Heisenberg spin-chain subject to a dephasing environmental interaction. We introduce new results from quantum information theory which enables the quantification of coherence and entanglement in a bi- and multipartite system. The calculated measures of these quantum effects can be linked to observables, such as magnetisation and total spin, with simulations of the model and using theoretical methods. We demonstrate that these observables can act as a proxy for the coherence and entanglement measures. The decay of both of these between the two local triplets can be monitored, enabling a clear definition of the spin-decoherence process in singlet fission.

physics.chem-ph↗

arXiv2017

Ultra-Fast Relaxation, Decoherence and Localization of Photoexcited States in $π$-Conjugated Polymers: A TEBD Study

The exciton relaxation dynamics of photoexcited electronic states in poly($p$-phenylenevinylene) (PPV) are theoretically investigated within a coarse-grained model, in which both the exciton and nuclear degrees of freedom are treated quantum mechanically. The Frenkel-Holstein Hamiltonian is used to describe the strong exciton-phonon coupling present in the system, while external damping of the internal nuclear degrees of freedom are accounted for by a Lindblad master equation. Numerically, the dynamics are computed using the time evolving block decimation (TEBD) and quantum jump trajectory techniques. The values of the model parameters physically relevant to polymer systems naturally lead to a separation of time scales, with the ultra-fast dynamics corresponding to energy transfer from the exciton to the internal phonon modes (i.e., the C-C bond oscillations), while the longer time dynamics correspond to damping of these phonon modes by the external dissipation. Associated with these time scales, we investigate the following processes that are indicative of the system relaxing onto the emissive chromophores of the polymer: 1) Exciton-polaron formation occurs on an ultra-fast time scale, with the associated exciton-phonon correlations present within half a vibrational time period of the C-C bond oscillations. 2) Exciton decoherence is driven by the decay in the vibrational overlaps associated with exciton-polaron formation, occurring on the same time scale. 3) Exciton density localization is driven by the external dissipation, arising from `wavefunction collapse' occurring as a result of the system-environment interactions. Finally, we show how fluorescence anisotropy measurements can be used to investigate the exciton decoherence process during the relaxation dynamics.

physics.chem-ph↗