# William Barford

## Professor William Barford

### Professor of Theoretical Chemistry

## Quantum Processes in Macromolecular Systems

My research is the theoretical study of quantum processes in macromolecular systems, in particular in π-conjugated molecules. Conjugated molecules (e.g., polymers, nanotubes, porphyrins and DNA) occur widely in many synthetic and biological systems; for example, in polymer optoelectronic devices and light harvesting complexes.

These systems are characterised by both strong electron-electron interactions and electron-nuclear coupling, and are subject to spatial and temporal disorder. Moreover, they are strongly coupled to their 'noisy' environment. Part of my research is focussed on understanding the effect of these interactions on the electronic and optical properties of conjugated macromolecules. Another goal is to understand excited state dynamics, from ultrafast decoherence and localization processes to post-ps exciton migration and diffusion, and to relate these predictions to experimental observables.

These goals are being pursued using a variety of theoretical methods and computational techniques (e.g., DMRG (including time-dependent DMRG), MPS methods and CI-S) on a wide variety of models (e.g., Pariser-Parr-Pople, Hubbard-Peierls and Frenkel-Holstein models).

**Singlet fission in carotenoids**

Singlet fission in polyacenes and carotenoids has the potential to enhance the efficiency of photovoltaic devices. It is also a fascinating process in its own right, because it requires an understanding of the roles of electronic correlation, electron-phonon coupling, and the coupling of a quantum system to its environment. My group, in collaboration with experimentalists at the University of Sheffield, is applying the t-DMRG and TEBD methods to model Hamiltonians in order to understand this mechanism in polyenes (especially carotenoids).

There are two complementary strands to this work. First, we are investigating state interconversion from the optically excited singlet state (S_{2}) to triplet-pair states (see *J. Phys. Chem. Lett.* **13**, 1344 (2022)). Second, we are investigating decoherence and disentanglement of triplet-pair states to become spin-uncorrelated (non-geminate) triplet pairs (see Phys Rev B **102**, 035134 (2020)).

**Modelling exciton and charge dynamics**

Exciton dynamics in conjugated polymers is a fascinating and complex topic, as it encompasses multiple time and length scales, and is determined by many factors, including electron-nuclear coupling, disorder and system-bath interactions. In recent years the development of realistic coarse-grained exciton-phonon models coupled to sophisticated numerical techniques and theoretical insights have led to a wide-range of theoretical predictions of exciton dynamics, from ultrafast intrachain relaxation and decoherence to sub-ns Forster-type interchain transfer and diffusion. These predictions can now be used to interpret a wide-range of time-resolved spectroscopic experiments. See here for a review.

**Developing the DMRG method for quantum chemistry and condensed matter physics**

Density matrix renormalization group (DMRG), matrix products states (MPS), and their associated time-dependent methods, are extremely powerful computational tools to solve one-dimensional quantum systems. As such, they are particularly suited to study conjugated polymers. My group is pioneering these methods to study one-dimensional linear conjugated systems. We are also developing computational methods to simulate dynamics in open-quantum systems. See this paper for an application of DMRG methods to simulate photoexcited state dynamics in carotenoids.

William Barford is a professor of theoretical chemistry and a tutorial fellow in physical chemistry at Balliol College. His theoretical research interests have encompassed soft condensed matter and high temperature superconductors, but for the last 20 years have been focussed on the electronic and optical properties of conjugated polymers. He is the author of Electronic and Optical Properties of Conjugated Polymers, published by Oxford University Press.

Professor Barford obtained a BSc degree in physics from the University of Sheffield and a PhD in theoretical condensed matter physics from the University of Cambridge. He undertook postdoctoral research at the Rutherford Appleton Laboratory and the University of Chicago. He was a lecturer, senior lecturer and latterly reader in physics in Sheffield before being appointed to his current post in Oxford in 2006. He has also been a Gordon Godfrey Visiting Fellow at the University of New South Wales and a Visiting Professor at MIT.

**Quantum Processes in Macromolecular Systems **

π-conjugated molecules (e.g., polymers, nanotubes, porphyrins and DNA) occur widely in many synthetic and biological systems; for example, in polymer optoelectronic devices and light harvesting complexes.

These systems are characterised by both strong electron-electron interactions and electron-nuclear coupling, and are subject to spatial and temporal disorder. Part of my research is focussed on understanding the effect of these interactions on the electronic and optical properties of conjugated macromolecules. Another goal is to understand excited state dynamics, from ultrafast decoherence and localization processes to post-ps exciton migration and diffusion, and to relate these predictions to experimental observables.

Further aims are to predict how the electronic and optical behaviour of condensed phase systems are determined by the multiscale structures of the component molecules, as well as the inverse problem: how experimental observables coupled with theoretical modelling can help determine multiscale structures.

These goals are being pursued using a variety of theoretical methods and computational techniques (e.g., DMRG (including time-dependent DMRG), MPS methods, and CI-S) on a wide variety of models (e.g., Pariser-Parr-Pople, Hubbard-Peierls, and Frenkel-Holstein models).

Recent work is listed in Selected Publications.

I am a member of the Oxford Theoretical Chemistry Group and the Centre for Doctoral Training in Theory and Modelling in Chemical Sciences (TMCS).

Students interested in Part II projects are welcome to contact me about potential projects. Prospective DPhil/PhD students should apply here or to the CDT in TMCS.

**My current projects include:**

**Singlet fission in carotenoids**

Singlet fission in polyacenes and carotenoids has the potential to enhance the efficiency of photovoltaic devices. It is also a fascinating process in its own right, because it requires an understanding of the roles of electronic correlation, electron-phonon coupling, and the coupling of a quantum system to its environment. My group, in collaboration with experimentalists at the University of Sheffield, is applying the t-DMRG and TEBD methods to model Hamiltonians in order to understand this mechanism in polyenes (especially carotenoids).

There are two complementary strands to this work. First, using t-DMRG, we are investigating state interconversion from the optically excited singlet state (S_{2}) to triplet-pair states (see *J. Phys. Chem. Lett.* **13**, 1344 (2022*)*). Second, we are investigating the decoherence and dissociation of triplet-pair states to become spin-uncorrelated (non-geminate) triplet pairs (see *Phys Rev B 102, 035134* (2020)).

**Modelling exciton and charge dynamics in conformationally disordered polymers in a dissipative environment**

The images shown below are surface plots of exciton wavefunctions, Φ, in the light emitting polymer poly(para-phenylene) (shown above). r is the electron-hole separation and R is the electron-hole centre-of-mass position (in monomer units). The 1^{1}B_{1u} exciton is also known as the (singlet) 'Frenkel' exciton, while the 2^{1}A_{g} exciton is also known as the (singlet) 'charge-transfer' exciton; see *J. Chem. Phys.* **129**, 164716 (2008) or my book for further details.

The image shown below represents the formation of an exciton-polaron quasiparticle after photoexcitation of a conjugated polymer, caused by the coupling of the exciton to C-C bond vibrations. Ultrafast exciton-polaron formation causes ultrafast exciton decoherence and manifests itself as time-resolved fluorescence depolarization; see *J. Chem. Phys*. **148**, 034901 (2018).

**Developing theories of optical transitions in π-conjugated systems**

The figure below shows the theoretical emission spectra of PPV as a function of torsonal disorder. The ratio of the 0-0 to 0-1 vibronic transitions is a measure of the average chromophore size, which decreases with increasing disorder; see *J. Chem. Phys*. **141**, 164102 (2014).

**Developing the density matrix renormalization group (DMRG) method for quantum chemistry and condensed matter physics**

DMRG, matrix products states (MPS), and their associated time-dependent methods, are extremely powerful computational tools to solve one-dimensional quantum systems. As such, they are particularly suited to study conjugated polymers. We are developing these techniques to model photoexcited state dynamics and the associated observables in highly-correlated electron systems subject to strong electron-phonon coupling. See this paper for an application of DMRG methods to simulate photoexcited state dynamics in carotenoids.

**Group Members:**

- Isabel Gonzalvez (5th year DPhil student): Exciton dynamics and spectroscopy of π-conjugated polymers
- Dilhan Manawadu (4th year DPhil student): Dynamics of photoexcited states in carotenoids
- Timothy Georges (1st year DPhil student): Singlet fission in carotenoids
- Cameron Chambers (Part II student): Singlet triplet-pair dissociation and decoherence in carotenoid dimers

My full publication list can be found here.

************************************************************************************

**Recent Papers**

Photoexcited state dynamics and singlet fission in carotenoids

D. Manawadu, T. N. Georges and W. Barford, *J. Phys. Chem. A*. **127**, 1342 (2023)

Exciton dynamics in conjugated polymer systems

W. Barford, *Frontiers in Physics* (2022)

Theory of the dark state of polyenes and carotenoids

W. Barford, *Phys. Rev. B ***106**, 035201 (2022)

Singlet triplet-pair production and possible singlet-fission in carotenoids

D. Manawadu, D. J. Valentine, M. Marcus and W. Barford, *J. Phys. Chem. Lett.* **13**, 1344 (2022)

Thermally driven polaron transport in conjugated polymers

L. Berencei, W. Barford, and S. R. Clark, *Phys. Rev. B ***105**, 014303 (2022)

Measuring time-dependent induced quantum coherences via two-dimensional coherence spectroscopy

W. Barford, A. N. Arber, F. McLennan and M. Marcus, *Phys. Rev. A* **104**, 063517 (2021)

************************************************************************************

**Singlet Fission in Polyenes**

Photoexcited state dynamics and singlet fission in carotenoids

D. Manawadu, T. N. Georges and W. Barford, *J. Phys. Chem. A*. *xxx*, xxx (2023)

Theory of the dark state of polyenes and carotenoids

W. Barford, *Phys. Rev. B ***106**, 035201 (2022)

Singlet triplet-pair production and possible singlet-fission in carotenoids

D. Manawadu, D. J. Valentine, M. Marcus and W. Barford, *J. Phys. Chem. Lett.* **13**, 1344 (2022)

Triplet-triplet decoherence in singlet fission

M. Marcus and W. Barford, *Phys Rev B 102, 035134* (2020)

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

D. J. Valentine, D. Manawadu and W. Barford, *Phys Rev B 102, 125107* (2020

*)*

************************************************************************************

**Spectroscopy of Conjugated Polymers**

Measuring time-dependent induced quantum coherences via two-dimensional coherence spectroscopy

W. Barford, A. N. Arber, F. McLennan and M. Marcus, *Phys. Rev. A* **104**, 063517 (2021)

Extracting structural information from MEH-PPV optical spectra

J. D. Milward, M. Marcus, A. Köhler and W. Barford,** ***J. Chem. Phys.*** 149**, 044903 (2018)

Theory of optical transitions in curved chromophores

W. Barford and M. Marcus, *J. Chem. Phys*. **145**, 124111, (2016)

Theory of optical transitions in conjugated polymers I: Ideal systems

W. Barford and M. Marcus, *J. Chem. Phys*. **141**, 164101 (2014)

Theory of optical transitions in conjugated polymers II: Real systems

M. Marcus, O. R. Tozer, and W. Barford, *J. Chem. Phys*. **141**, 164102 (2014)

************************************************************************************

**Exciton Localization in Disordered Conjugated Polymers**

Polarons in π-conjugated polymers: Anderson or Landau?

W. Barford, M. Marcus and O. R. Tozer, *J. Phys. Chem. A ***120**, 615 (2016)

Local exciton ground states in disordered polymers

D. V. Makhov and W. Barford, *Phys. Rev. B* **81**, 165201 (2010)

Exciton localization in polymers with static disorder

W. Barford and D. Trembath, *Phys. Rev. B* **80**, 165418 (2009)

************************************************************************************

**Exciton Dynamics in Conjugated Polymers**

Ultrafast fluorescence depolarization in conjugated polymers

I. Gonzalvez Perez and W. Barford, *J. Phys. Chem. Lett.* **12**, 5344 (2021)

Torsionally induced exciton localization and decoherence in *π*-conjugated polymers

W. Barford and J. R. Mannouch,* J. Chem. Phys*. **149**, 214107 (2018)

Ultrafast relaxation, decoherence, and localization of photoexcited states in π-conjugated polymers

J. R. Mannouch, W. Barford and S. Al-Assam*, J. Chem. Phys*. **148**, 034901 (2018)

Intrachain exciton dynamics in conjugated polymer chains in solution

O. R. Tozer and W. Barford, *J. Chem. Phys*. **143**, 084102 (2015)

Theory of exciton transfer and diffusion in conjugated polymers

W. Barford and O. R. Tozer, *J. Chem. Phys*. **141**, 164103 (2014)

************************************************************************************

**Electronic Processes in Conjugated Polymers**

Spin-orbit interactions between inter-chain excitations in conjugated polymers

W. Barford, R. J. Bursill and D. V. Makhov, *Phys. Rev. B* **81**, 35206 (2010)

Exciton transfer integrals between polymer chains

W. Barford, *J. Chem. Phys.* **126**, 134905 (2007)

Theory of the singlet exciton yield in light emitting polymers

W. Barford, *Phys Rev B* **70**, 205204 (2004)

************************************************************************************

**Excited State Properties of Conjugated Polymers**

Excited states in polydiacetylene chains: A density-matrix-renormalization-group study

G. Barcza, W. Barford, F. Gebhard, and O. Legeza, *Phys. Rev. B* **87**, 245116 (2013)

R. J. Bursill and W. Barford, *J. Chem. Phys.* **130**, 234302 (2009)

Excitons in conjugated polymers: wavefunctions, symmetries and quantum numbers

W. Barford and N. Paiboonvorachat, *J. Chem. Phys.* **129**, 164716 (2008)

************************************************************************************

**Charge Transport in Conjugated Polymers**

Thermally driven polaron transport in conjugated polymers

L. Berencei, W. Barford, and S. R. Clark, *Phys. Rev. B ***105**, 014303 (2022)

Realistic model of charge mobility in π-conjugated polymer systems

L. Berencei, A. Grout-Smith, J. E. Poole and W. Barford, *J. Chem. Phys.* **151**, 064120 (2019)

************************************************************************************

**Electron-Phonon Coupling**

Localization of large polarons in the disordered Holstein model

O. R. Tozer and W. Barford,* Phys. Rev. B ***89**, 155434 (2014)

Quantized lattice dynamic effects on the Peierls transition of the extended Hubbard model

C. J. Pearson, W. Barford and R. J. Bursill, *Phys. Rev. B* **83**, 195105 (2011)

Quantized lattice dynamic effects on the spin-Peierls transition

C. J. Pearson, W. Barford and R. J. Bursill, *Phys. Rev. B* **82**, 144408 (2010)

************************************************************************************

**Review Articles**

Exciton dynamics in conjugated polymers systems

W. Barford, *Frontiers in Physics* (2022)

W. Barford and M. Marcus, *J. Chem. Phys*. **146**, 130902, (2017)

Excitons in conjugated polymers: A tale of two particles

W. Barford, *J. Phys. Chem. A* **117**, 2665 (2013)

************************************************************************************

**Book**

Electronic and Optical Properties of Conjugated Polymers

W. Barford, Oxford University Press (2013)

Reviews in Physics Today and Contemporary Physics