arXiv subjects

Timothy J. H. Hele

Publications and source records attributed to Timothy J. H. Hele.

At least 19 recordsLinked to original sources

arXiv2026

On the Electronic Path-Integral Normal Modes of the Spin-Mapping Representation of Nonadiabatic Dynamics

Nonadiabatic Matsubara dynamics has been proposed in both the Meyer-Miller-Stock-Thoss (MMST) and spin-mapping representations, whereby the dynamics are truncated in the higher path-integral normal modes of the nuclear degrees of freedom, but no truncation is performed in the electronic variables. In contrast to single-surface Matsubara dynamics, these methods do not appear to conserve the Quantum Boltzmann Distribution (QBD) for general systems. Recently, it was shown that truncating in the electronic path-integral normal modes of the MMST representation does not lead to conservation of the QBD for a single trajectory or accurate computation of a correlation function. Here, the electronic path-integral normal modes in the spin-mapping representation are investigated. We focus on a two-level system although we expect our findings to be applicable to any number of electronic states. We find, perhaps surprisingly, that the higher normal modes of the spin-vector $z$-component, the difference in state populations, are constrained by the QBD, that the time-evolved state population observable is a function of only the spin-mapping centroid, and that the full $N$-bead computational results are replicated using only the spin-mapping centroid, leading to accurate, QBD conserving dynamics. While at present these results are not a generally-applicable method, we believe this may explain the recent success of spin-mapping approaches compared to MMST approaches, %To our knowledge, this is the first method obtaining conservation of the QBD when truncating in electronic normal modes and should aid the future derivation of highly accurate and Quantum Boltzmann conserving nonadiabatic dynamics methods.

physics.chem-ph↗

arXiv2026

On the Symplectic Propagation of the Spin-MInt Algorithm for Non-Adiabatic Quantum Dynamics

Mapping methods are often used for the numerical simulation of nonadiabatic systems by propagating classical mapping variable trajectories. A recently popularised mapping method is spin-mapping, whose mapping variables arise from quantum mechanical operators with symmetries described by a Lie-Poisson algebra. Simulating the classical-like dynamics of spin-mapping systems accurately is generally challenging, with many methods unable to preserve the underlying geometric structure of the symplectic form. The Spin-MInt algorithm is a recently proposed algorithm propagating spin-mapping variables, with a direct proof of symplecticity existing only for 2 electronic states. Here, we directly prove the symplecticity of the Spin-MInt algorithm for a general $K$ electronic states. A review of the symplectic nature of coadjoint orbits of the $\mathfrak{su}(K)$ Lie-Poisson algebra provides the framework needed to understand symplecticity of the Spin-MInt algorithm in this general case. The symplecticity of the method on the associated coadjoint orbit is then shown for what we believe to be the first time via an explicit verification of the symplecticity condition $\mathbf{MJ}\mathbf{M}^\textrm{T}=\mathbf{J}$ exploiting the Lie-Poisson structure of the system. To our knowledge, this is the first time the monodromy matrix for the Spin-MInt algorithm has been explicitly stated using canonical coordinates on the coherent state manifold for a general number of states. We hope that this will assist the development of classical-like spin-mapping methods which might utilise elements of the monodromy matrix, and inform future work on similar symplectic algorithms for coupled and uncoupled Lie-Poisson systems.

physics.chem-ph↗

arXiv2026

Developing fast, accurate and spin pure calculations of organic diradical electronic structure

Organic diradical molecules have emerged in recent years as highly promising candidates for next generation optoelectronic and quantum information technologies. As efforts continue to synthesise diradicals with unique photophysical properties, developing our theoretical understanding of their complex electronic structure is crucial to enable rational design strategies. However, existing computational tools struggle to properly describe the multi-reference character of diradical electronic states while also preserving a low computational scaling that enables fast calculations on large emissive diradicals. This work presents a new computational method, termed Diradical Extended Restricted Open-shell PPP (D-ExROPPP) theory, which we show yields accurate and spin-pure electronic states at a very low computational cost relative to existing approaches. This is achieved by implementing a novel, spin-adapted configuration interaction approach within the semi-empirical Pariser-Parr-Pople framework. D-ExROPPP is then used to study the electronic structure of three prototypical organic diradicals, and benchmarked against results from computationally intensive, post-Hartree-Fock methods. Excitation energies for these molecules are predicted that show a similar level of accuracy as high-level ab-initio calculations, while requiring up to five orders of magnitude less computational time. We further apply D-ExROPPP to a number of recently reported stable, emissive, organic diradicals. In the majority of cases, electronic transitions measured in experimental UV-vis spectra are reproduced with qualitative accuracy and the spin states involved can be reliably assigned. Together, these results establish D-ExROPPP as a promising new tool for efficiently predicting and interpreting the photophysics of organic diradical molecules.

physics.chem-ph↗

arXiv2026

The Spin-MInt Algorithm: an Accurate and Symplectic Propagator for the Spin-Mapping Representation of Nonadiabatic Dynamics

Mapping methods, including the Meyer-Miller-Stock-Thoss (MMST) mapping and spin-mapping, are commonly utilised to simulate nonadiabatic dynamics by propagating classical mapping variable trajectories. Recent work confirmed the Momentum Integral (MInt) algorithm is the only known symplectic algorithm for the MMST Hamiltonian. To our knowledge, no symplectic algorithm has been published for the spin-mapping representation without obtaining Cartesian variables and utilising the MInt algorithm. Here, we present the Spin-MInt algorithm which directly propagates the spin-mapping variables. First, we consider a two-level system which maps onto a spin-vector on a Bloch sphere. Despite the spin-variables being non-canonical, we rigorously prove the Spin-MInt is symplectic using a canonical variable transformation. We determine that the Spin-MInt is a symmetrical, second-order, time-reversible, angle invariant and geometric structure preserving algorithm. Computationally, for a one-dimensional spin-boson model, the Spin-MInt and MInt algorithms are symplectic, satisfy Liouville's theorem, provide second-order energy conservation and are more accurate than a previously-published angle-based algorithm. We additionally present accurate correlation functions for a multi-dimensional spin-boson model. We also extend this methodology to a general number of electronic states and present accurate population results for a three-state Morse potential. The Spin-MInt is faster than the MInt algorithm for all tested models, particularly so for large nuclear degrees of freedom. We believe this to be the first known symplectic algorithm for propagating the nonadiabatic spin-mapping Hamiltonian and one of the first rigorously symplectic algorithms in the case of non-trivial coupling between canonical and spin systems. These results should guide and improve future simulations.

physics.chem-ph↗

arXiv2025

On the electronic path integral normal modes of the Meyer-Miller-Stock-Thoss representation of nonadiabatic dynamics

Accurate and efficient simulation of nonadiabatic dynamics is highly desirable for understanding charge and energy transfer in complex systems. A key criterion for obtaining an accurate method is conservation of the Quantum Boltzmann Distribution (QBD). For a single surface, Matsubara dynamics is known to conserve the QBD, as a consequence of truncating the dynamics in the higher normal modes of the imaginary-time path integral. Recently, a nonadiabatic Matsubara (NA-Mats) dynamics has been proposed (J. Chem. Phys., 2021, 154, 124124) which truncates in the normal modes of the nuclear variables but not in the electronic variables, which are described with the Meyer-Miller-Stock-Thoss (MMST) representation. Surprisingly, this NA-Mats method does not appear to conserve the QBD for a general system. This poses the question of the effect of truncating the higher path integral normal modes of the electronic variables in the MMST representation. In this article, we present what we believe is the first study of electronic normal modes of the MMST representation. We find that observables are not usually a function of a finite number of normal modes and that the higher normal modes are not constrained by the distribution, unlike in conventional nuclear normal modes. Furthermore, truncating the dynamics in MMST normal modes leads to inaccurate correlation functions and while the QBD appears conserved for an ensemble of trajectories, it is not for a single trajectory. Overall, this suggests that MMST path integral normal modes are not optimal for obtaining an accurate, QBD conserving nonadiabatic dynamics method.

physics.chem-ph↗

arXiv2025

Coulombic control of charge transfer in luminescent radicals with long-lived quartet states

Excitons in organic materials are emerging as an attractive platform for tunable quantum technologies. Structures with near-degenerate doublet and triplet excitations in linked trityl radical, acene and carbazole units can host quartet states. These high spin states can be coherently manipulated, and later decay radiatively via the radical doublet transition. However, this requires controlling the deexcitation pathways of all metastable states. Here we establish design rules for efficient quartet generation in luminescent radicals, using different connection arrangements of the molecular units. We discover that electronic coupling strength between these units dictates luminescence and quartet formation yields, particularly through the energetics of an acene-radical charge transfer state, which we tune Coulombically. This state acts as a source of non-radiative decay when acene-radical separation is small, but facilitates doublet-quartet spin interconversion when acene-radical separation is large. Using these rules we report a radical-carbazole-acene material with 55% luminescence yield, where 94% of emitting excitons originate from the quartet at microsecond times. This reveals the central role of molecular topology in luminescent quantum materials.

cond-mat.mtrl-sci↗

arXiv2025

Learning Radical Excited States from Sparse Data

Emissive organic radicals are currently of great interest for their potential use in the next generation of highly efficient organic light emitting diode (OLED) devices and as molecular qubits. However, simulating their optoelectronic properties is challenging, largely due to spin-contamination and the multireference character of their excited states. Here we present a data-driven approach where, for the first time, the excited electronic states of organic radicals are learned directly from experimental excited state data, using a much smaller amount of data than typically required by Machine Learning. We adopt ExROPPP, a fast and spin-pure semiempirical method for calculation of the excited states of radicals, as a surrogate physical model for which we learn the optimal set of parameters. To achieve this we compile the largest known database of organic radical geometries and their UV-vis data, which we use to train our model. Our trained model gives Root Mean Square (RMS) and mean absolute errors for excited state energies of 0.24 and 0.16 eV respectively, improving hugely over ExROPPP with literature parameters. Four new organic radicals are synthesised and we test the model on their spectra, finding even lower errors and similar correlation as for the testing set. This model paves the way for the high throughput discovery of next generation radical-based optoelectronics.

physics.chem-ph↗

arXiv2024

ExROPPP: Fast, Accurate and Spin-Pure Calculation of the Electronically Excited States of Organic Hydrocarbon Radicals

Recent years have seen an explosion of interest in organic radicals due to their promise for highly efficient organic light-emitting diodes (OLEDs) and molecular qubits. However, accurately and inexpensively computing their electronic structure has been challenging, especially for excited states, due to the spin-contamination problem. Furthermore, while alternacy or `pseudoparity' rules have guided the interpretation and prediction of the excited states of closed-shell hydrocarbons since the 1950s, similarly general rules for hydrocarbon radicals have not to our knowledge yet been found. In this article we present solutions to both of these challenges. We firstly combine the extended configuration interaction singles (XCIS) method with Pariser-Parr-Pople (PPP) theory to obtain a method which we call ExROPPP (Extended Restricted Open-shell PPP theory). We find that ExROPPP computes spin-pure excited states of hydrocarbon radicals with comparable accuracy to experiment as high-level GMC-QDPT calculations but at a computational cost that is at least two orders of magnitude lower. We then use ExROPPP to derive widely-applicable rules for the spectra of alternant hydrocarbon radicals which are completely consistent with our computed results. These findings pave the way for the highly accurate and efficient computation and prediction of the excited states of organic radicals.

physics.chem-ph↗

arXiv2023

Which Algorithm Best Propagates the Meyer-Miller-Stock-Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics?

A common strategy to simulate mixed quantum-classical dynamics is by propagating classical trajectories with mapping variables, often using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian or the related spin-mapping approach. When mapping the quantum subsystem, the coupled dynamics reduce to a set of equations of motion to integrate. Several numerical algorithms have been proposed, but a thorough performance comparison appears to be lacking. Here, we compare three time-propagation algorithms for the MMST Hamiltonian: the Momentum Integral (MInt) (arXiv:1709.07474), the Split-Liouvillian (SL) (arXiv:1609.00644), and the algorithm in arXiv:1201.1042 that we refer to as the Degenerate Eigenvalue (DE) algorithm due to the approximation required during derivation. We analyse the accuracy of individual trajectories, correlation functions, energy conservation, symplecticity, Liouville's theorem and the computational cost. We find that the MInt algorithm is the only rigorously symplectic algorithm. However, comparable accuracy at a lower computational cost can be obtained with the SL algorithm. The approximation implicitly made within the DE algorithm conserves energy poorly, even for small timesteps, and thus leads to slightly different results. These results should guide future mapping-variable simulations.

physics.chem-ph↗

arXiv2022

Inverse molecular design from first principles: tailoring organic chromophore spectra for optoelectronic applications

The discovery of molecules with tailored optoelectronic properties such as specific frequency and intensity of absorption or emission is a major challenge in creating next-generation organic light-emitting diodes (OLEDs) and photovoltaics. This raises the question: how can we predict a potential chemical structure from these properties? Approaches that attempt to tackle this inverse design problem include virtual screening, active machine learning and genetic algorithms. However, these approaches rely on a molecular database or many electronic structure calculations, and significant computational savings could be achieved if there was prior knowledge of (i) whether the optoelectronic properties of a parent molecule could easily be improved and (ii) what morphing operations on a parent molecule could improve these properties. In this perspective we address both of these challenges from first principles. We firstly adapt the Thomas-Reiche-Kuhn sum rule to organic chromophores and show how this indicates how easily the absorption and emission of a molecule can be improved. We then show how by combining electronic structure theory and intensity borrowing perturbation theory we can predict whether or not the proposed morphing operations will achieve the desired spectral alteration, and thereby derive widely-applicable design rules. We go on to provide proof-of-concept illustrations of this approach to optimizing the visible absorption of acenes and the emission of radical OLEDs. We believe this approach can be integrated into genetic algorithms by biasing morphing operations in favour of those which are likely to be successful, leading to faster molecular discovery and greener chemistry.

physics.chem-ph↗

arXiv2022

Electronic energies from coupled fermionic 'Zombie' states imaginary time evolution

Zombie States are a recently introduced formalism to describe coupled coherent Fermionic states which address the Fermionic sign problem in a computationally tractable manner. Previously it has been shown that Zombie States with fractional occupations of spin-orbitals obeyed the correct Fermionic creation and annihilation algebra and presented results for real-time evolution [Dmitrii V. Shalashilin, J. Chem. Phys. 148, 194109 (2018)]. In this work we extend and build on this formalism by developing efficient algorithms for evaluating the Hamiltonian and other operators between Zombie States and address their normalization. We also show how imaginary time propagation can be used to find the ground state of a system. We also present a biasing method, for setting up a basis set of random Zombie States, that allow much smaller basis sizes to be used while still accurately describing the electronic structure Hamiltonian and its ground state and describe a technique of wave function "cleaning" which removes the contributions of configurations with the wrong number of electrons, improving the accuracy further. We also show how low-lying excited states can be calculated efficiently using a Gram-Schmidt orthogonalization procedure.The proposed algorithm of imaginary time propagation on a biased random grids of Zombie States may present an alternative to existing Quantum Monte Carlo methods.

physics.comp-ph↗

arXiv2021

Singlet and triplet to doublet energy transfer: improving organic light-emitting diodes with radicals

Organic light-emitting diodes (OLEDs) must be engineered to circumvent the efficiency limit imposed by the 3:1 ratio of triplet to singlet exciton formation following electron-hole capture. Here we show the spin nature of luminescent radicals such as TTM-3PCz allows direct energy harvesting from both singlet and triplet excitons through energy transfer, with subsequent rapid and efficient light emission from the doublet excitons. This is demonstrated with a model Thermally-Activated Delayed Fluorescence (TADF) organic semiconductor, 4CzIPN, where reverse intersystem crossing from triplets is characteristically slow (50% emission by 1 microsecond). The radical:TADF combination shows much faster emission via the doublet channel (80% emission by 100 ns) than the comparable TADF-only system, and sustains higher electroluminescent efficiency with increasing current density than a radical-only device. By unlocking energy transfer channels between singlet, triplet and doublet excitons, further technology opportunities are enabled for optoelectronics using organic radicals.

physics.chem-ph↗

arXiv2021

Systematic improvement of molecular excited state calculations by inclusion of nuclear quantum motion: a mode-resolved picture and the effect of molecular size

The energies of molecular excited states arise as solutions to the electronic Schrödinger equation and are often compared to experiment. At the same time, nuclear quantum motion is known to be important and to induce a red-shift of excited state energies. However, it is thus far unclear whether incorporating nuclear quantum motion in molecular excited state calculations leads to a systematic improvement of their predictive accuracy, making further investigation necessary. Here we present such an investigation by employing two first-principles methods for capturing the effect of quantum fluctuations on excited state energies, which we apply to the Thiel set of organic molecules. We show that accounting for zero-point motion leads to much improved agreement with experiment, compared to `static' calculations which only account for electronic effects, and the magnitude of the red-shift can become as large as 1.36 eV. Moreover, we show that the effect of nuclear quantum motion on excited state energies largely depends on the molecular size, with smaller molecules exhibiting larger red-shifts. Our methodology also makes it possible to analyze the contribution of individual vibrational normal modes to the red-shift of excited state energies, and in several molecules we identify a limited number of modes dominating this effect. Overall, our study provides a foundation for systematically quantifying the shift of excited state energies due to nuclear quantum motion, and for understanding this effect at a microscopic level.

physics.chem-ph↗

arXiv2019

Environmental Control of Triplet Emission in Donor-Bridge-Acceptor Organometallics

Carbene-metal-amides (CMAs) are a promising family of donor-bridge-acceptor molecular charge-transfer emitters for organic light-emitting diodes (OLEDs). Here a universal approach is introduced to tune the energy of their charge-transfer emission. A shift of up to 210 meV is achievable in the solid state via dilution in a polar host matrix. The origin of this shift has two components: constraint of thermally activated triplet diffusion, and electrostatic interactions between the guest molecules and the polar host. This allows the emission of mid-green CMA archetypes to be blue shifted without chemical modifications. Monte-Carlo simulations based on a Marcus-type transfer integral successfully reproduce the concentration- and temperature-dependent triplet diffusion process, and reveal a substantial shift in the ensemble density of states in polar hosts. In gold-bridged CMAs this substantial shift does not lead to a significant change in luminescence lifetime, thermal activation energy, reorganisation energy or intersystem crossing rate. These discoveries thus offer new experimental and theoretical insight in to the coupling between the singlet and triplet manifolds in these materials. Similar emission tuning can be achieved in related materials where chemical modification is used to modify the charge-transfer energy.

physics.app-ph↗

arXiv2018

Anticipating acene-based chromophore spectra with molecular orbital arguments

Recent synthetic studies on the organic molecules tetracene and pentacene have found certain dimers and oligomers to exhibit an intense absorption in the visible region of the spectrum which is not present in the monomer or many previously-studied dimers. In this article we combine experimental synthesis with electronic structure theory and spectral computation to show that this absorption arises from an otherwise dark charge-transfer excitation 'borrowing intensity' from an intense UV excitation. Further, by characterizing the role of relevant monomer molecular orbitals, we arrive at a design principle that allows us to predict the presence or absence of an additional absorption based on the bonding geometry of the dimer. We find this rule correctly explains the spectra of a wide range of acene derivatives and solves an unexplained structure-spectrum phenomenon first observed seventy years ago. These results pave the way for the design of highly absorbent chromophores with applications ranging from photovoltaics to liquid crystals.

physics.chem-ph↗

arXiv2018

Theoretical description of Carbene-Metal-Amides

Carbene-Metal-Amide light-emitting diodes have recently shown internal quantum efficiencies approaching 100%, and there has been substantial debate concerning the cause of their exceptionally high efficiency. Here we present a theoretical description of CMAs, showing how a simple three-atom model can predict the form of the HOMO and LUMO, determine the polarization of transitions and the feasibility of spin-orbit coupling, as well as the qualitative dependence of excited state energies and oscillator strength on the twist angle. These results clarify many of the claims concerning CMAs and pave the way for the design of more efficient devices.

physics.chem-ph↗

arXiv2017

Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation

We extend the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), a semiclassical method for computing real-time correlation functions, to electronically nonadiabatic systems using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian to treat electronic and nuclear degrees of freedom (dofs) within a consistent dynamic framework. We introduce an efficient symplectic integration scheme, the MInt algorithm, for numerical time-evolution of the nuclear and electronic phase space variables as well as the Monodromy matrix, under the non-separable MMST Hamiltonian. We then calculate the probability of transmission through a curve-crossing in model two-level systems and show that in the quantum limit MQC-IVR is in good agreement with the exact quantum results, whereas in the classical limit the method yields results in keeping with mean-field approaches like the Linearized Semiclassical IVR. Finally, exploiting the ability of MQC-IVR to quantize different dofs to different extents, we present a detailed study of the extents to which quantizing the nuclear and electronic dofs improves numerical convergence properties without significant loss of accuracy.

physics.chem-ph↗

arXiv2017

Thermal quantum time-correlation functions from classical-like dynamics

Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally-measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here we review recent progress in the field with the development of methods including Centroid Molecular Dynamics (CMD), Ring Polymer Molecular Dynamics (RPMD) and Thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from `Matsubara dynamics', a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also rederive t->0+ quantum transition-state theory (QTST) in the Matsubara dynamics formalism showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.

physics.chem-ph↗