arXiv subjects

David E. Manolopoulos

Publications and source records attributed to David E. Manolopoulos.

At least 19 recordsLinked to original sources

arXiv2026

Economised path integrals

The Hessian of the ring polymer spring potential in the standard Trotter path integral is a $P\times P$ symmetric circulant matrix with a centroid eigenvalue of zero. All such matrices commute and are diagonalised by the same bead to normal mode transformation matrix, and their eigenvalues contain $\lceil P/2\rceil-1$ degenerate pairs by symmetry. However, this still leaves some freedom to improve on the Trotter approximation: one can optimise the remaining $\lfloor P/2\rfloor$ independent non-zero normal mode frequencies to fit the exact quantum mechanical radii of gyration of harmonic ring polymers with frequencies in the range $0\leω\leω_{\rm max}$, where $ω_{\rm max}$ is the maximum physical frequency in the problem of interest. The optimisation involves solving a simple least squares problem for the optimum (economised or "Eco") internal mode frequencies. The remainder of the calculation then proceeds in the same way as a Trotter path integral calculation. An example application to hexagonal ice shows that the convergence of the Eco path integral is comparable to that of the 4th order Suzuki-Chin path integral, but with purely 2nd order Trotter effort. There is no need to calculate the projected Hessians that arise in the Suzuki-Chin method by finite differences, there is no need to develop any new estimators for observables, and once the Eco frequencies have been calculated the implementation of the Eco path integral involves changing just a few lines of a Trotter path integral code. To provide a more impressive example we have implemented the Eco method in GPUMD and used it to converge the (negative) thermal expansion coefficient and the constant pressure heat capacity of MOF-5 with a machine-learned neuroevolution potential.

physics.chem-ph↗

arXiv2026

Nuclear quantum effects in the thermal conductivity of solid hydrogen

We use a combination of path integral and lattice dynamics methods to calculate the thermal conductivity of solid parahydrogen. Path integral molecular dynamics is first used to calculate a centroid potential of mean force at each temperature, on which a harmonic phonon basis is constructed using the finite displacement method. We then calculate anharmonic force constants on the centroid potential and solve the linearised phonon Boltzmann transport equation for the thermal conductivity. The resulting renormalised phonon dispersion curves, heat capacity, and thermal conductivity are all in remarkably good agreement with experimental measurements. We find that the heat transport is dominated by collective relaxon modes at low temperatures and cannot be captured by making the phonon relaxation time approximation. Indeed, quantitative agreement with the experimental thermal conductivity is only achieved when the nuclear quantum effects in the centroid potential of mean force, phonon boundary scattering, and hydrodynamic transport are all explicitly considered. This is also likely to be the case for other quantum crystals.

cond-mat.mtrl-sci↗

arXiv2026

Lattice thermal transport from phonon spectra beyond perturbation theory

We develop a molecular dynamics framework to compute the mode-resolved phonon spectral density from classical correlations of an annihilation-like phonon variable. For harmonic oscillators, classical molecular dynamics exactly reproduces the corresponding quantum Kubo-transformed correlator, providing the basis for extension to anharmonic systems. Using PbTe as a benchmark and Cs$_3$Bi$_2$I$_6$Cl$_3$ as a strongly anharmonic test case, we show that the method captures both quasiparticle and non-Lorentzian spectra beyond perturbative quasiparticle theory, while yielding thermal conductivity in good agreement with experiment. This framework provides a classical molecular dynamics route to mode-resolved phonon spectral densities for spectral Wigner heat transport in strongly anharmonic solids above their Debye temperatures.

cond-mat.mtrl-sci↗

arXiv2026

Path Integral Methods in Atomistic Modelling: An Introduction

This book provides an introduction to path integral methods and their application to modeling atomistic processes. The book covers both the foundational theory and recently developed simulation techniques. The text provides a self-contained resource and was originally developed for the CECAM schools on Path Integral Methods.

physics.chem-ph↗

arXiv2025

Two-dimensional electronic spectra from trajectory-based dynamics: pure-state Ehrenfest, spin-mapping, and mean classical path approaches

Two-dimensional electronic spectroscopy (2DES) provides a detailed picture of electronically nonadiabatic dynamics that can be interpreted with the aid of simulations. Here, we develop and contrast trajectory-based nonadiabatic dynamics approaches for simulating 2DES spectra. First, we argue that an improved pure-state Ehrenfest approach can be constructed by decomposing the initial coherence into a sum of equatorial pure states that contain equal contributions from the states in the coherence. We then use this framework to show how one can obtain a more accurate, but computationally more expensive, approximation to the third-order 2DES response function by replacing Ehrenfest dynamics with spin mapping during the pump-probe delay time. We end by comparing and contrasting the accuracy of these methods and the simpler mean classical path approximation in reproducing the exact linear, pump-probe, and 2DES spectra of two Frenkel exciton models: a coupled dimer system and the Fenna-Matthews-Olson (FMO) complex.

physics.chem-ph↗

arXiv2025

Nuclear quantum effects slow down the energy transfer in biological light-harvesting complexes

We assess how quantum-mechanical effects associated with high-frequency chromophore vibrations influence excitation energy transfer in biological light-harvesting complexes. We begin with a mixed quantum-classical theory that combines a quantum description of the electronic motion with a classical description of the nuclear motion in a way that is consistent with the quantum-classical equilibrium distribution. We then include nuclear quantum effects in this theory with a variational polaron transformation of the high frequency vibrational modes. This approach is validated by comparison with fully quantum mechanical benchmark calculations and then applied to three prototypical biological light-harvesting complexes. We find that high-frequency vibrations delay the energy transfer in the quantum treatment, but accelerate it in the classical treatment. For the inter-ring transfer in the light-harvesting complex 2 of purple bacteria, the transfer rate is a factor of 1.5 times slower in the quantum treatment than the classical. The transfer timescale in the Fenna--Matthews--Olson complex is essentially the same in both cases, whereas the transfer in light-harvesting complex II of spinach is 1.7 times slower in the quantum treatment. In all cases, the quantum mechanical long-time equilibrium populations of the chromophores are well reproduced by the classical treatment, suggesting that nuclear quantum effects are generally unimportant for the directionality of energy transfer. Nuclear quantum effects do however reduce the transfer rate in systems with large excitonic energy gaps and strong vibronic coupling to high-frequency vibrational modes.

physics.chem-ph↗

arXiv2024

Charge transport in organic semiconductors from the mapping approach to surface hopping

We describe how to simulate charge diffusion in organic semiconductors using a recently introduced mixed quantum-classical method, the mapping approach to surface hopping (MASH). In contrast to standard fewest-switches surface hopping, this method propagates the classical degrees of freedom deterministically on the most populated adiabatic electronic state. This correctly preserves the equilibrium distribution of a quantum charge coupled to classical phonons, allowing one to time-average along trajectories to improve the statistical convergence of the calculation. We illustrate the method with an application to a standard model for the charge transport in the direction of maximum mobility in crystalline rubrene. Because of its consistency with the equilibrium distribution, the present method gives a time-dependent diffusion coefficient that plateaus correctly to a long-time limiting value. The resulting mobility is somewhat higher than that of the relaxation time approximation, which uses a phenomenological relaxation parameter to obtain a non-zero diffusion coefficient from a calculation with static phonon disorder. However, it is very similar to the mobility obtained from Ehrenfest dynamics, at least in the parameter regimes we have investigated here. This is somewhat surprising because Ehrenfest dynamics overheats the electronic subsystem and is therefore inconsistent with the equilibrium distribution.

physics.chem-ph↗

arXiv2023

Exciton dynamics from the mapping approach to surface hopping: Comparison with Förster and Redfield theories

We compare the recently introduced multi-state mapping approach to surface hopping (MASH) with the Förster and Redfield theories of excitation energy transfer. Whereas Förster theory relies on weak coupling between chromophores, and Redfield theory assumes the electronic excitations to be weakly coupled to fast chromophore vibrations, MASH is free from any perturbative or Markovian approximations. We illustrate this with an example application to the rate of energy transfer in a Frenkel-exciton dimer, showing that MASH interpolates correctly between the opposing regimes in which the Förster and Redfield results are reliable. We then compare the three methods for a realistic model of the Fenna-Matthews-Olson complex with a structured vibrational spectral density and static disorder in the excitation energies. In this case there are no exact results for comparison so we use MASH to assess the validity of Förster and Redfield theories. We find that Förster theory is the more accurate of the two on the picosecond timescale, as has been shown previously for a simpler model of this particular light-harvesting complex. We also explore various ways to sample the initial electronic state in MASH and find that they all give very similar results for exciton dynamics.

physics.chem-ph↗

arXiv2023

Fast quasi-centroid molecular dynamics for water and ice

We describe how the fast quasi-centroid molecular dynamics (f-QCMD) method can be applied to condensed phase systems by approximating the quasi-centroid potential of mean force as a sum of inter- and intra-molecular corrections to the classical interaction potential. The corrections are found by using a regularised iterative Boltzmann inversion procedure to recover the inter- and intra-molecular quasi-centroid distribution functions obtained from a path integral molecular dynamics simulation. The resulting methodology is found to give good agreement with a previously published QCMD dipole absorption spectrum for liquid water, and satisfactory agreement for ice. It also gives good agreement with spectra from a recent implementation of CMD that uses a pre-computed elevated temperature potential of mean force. Modern centroid molecular dynamics methods therefore appear to be reaching a consensus regarding the impact of nuclear quantum effects on the vibrational spectra of water and ice.

physics.chem-ph↗

arXiv2023

A multi-state mapping approach to surface hopping

We describe a multiple electronic state adaptation of the mapping approach to surface hopping introduced recently by Mannouch and Richardson (J. Chem. Phys. 158, 104111 (2023)). This adaptation treats populations and coherences on an equal footing and is guaranteed to give populations in any electronic basis that tend to the correct quantum-classical equilibrium values in the long-time limit (assuming ergodicity). We demonstrate its accuracy by comparison with exact benchmark results for three- and seven-state models of the Fenna-Matthews-Olson complex, obtaining electronic populations and coherences that are significantly more accurate than those of fewest switches surface hopping and at least as good as those of any other semiclassical method we are aware of. Since these results were obtained by adapting the scheme of Mannouch and Richardson, we go on to compare our results with theirs for a variety of problems with two electronic states. We find that their method is sometimes more accurate, and especially so in the Marcus inverted regime. However, in other situations the accuracies are comparable, and since our scheme can be used with multiple electronic states it can be applied to a wider variety of systems.

physics.chem-ph↗

arXiv2023

A smooth basis for atomistic machine learning

Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighbourhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to expand the angular dependence of this density, but there is as yet no clear rationale to choose one radial basis over another. Here we investigate the basis that results from the solution of the Laplacian eigenvalue problem within a sphere around the atom of interest. We show that this generates the smoothest possible basis of a given size within the sphere, and that a tensor product of Laplacian eigenstates also provides the smoothest possible basis for expanding any higher-order correlation of the atomic density within the appropriate hypersphere. We consider several unsupervised metrics of the quality of a basis for a given dataset, and show that the Laplacian eigenstate basis has a performance that is much better than some widely used basis sets and is competitive with data-driven bases that numerically optimize each metric. In supervised machine learning tests, we find that the optimal function smoothness of the Laplacian eigenstates leads to comparable or better performance than can be obtained from a data-driven basis of a similar size that has been optimized to describe the atom-density correlation for the specific dataset. We conclude that the smoothness of the basis functions is a key and hitherto largely overlooked aspect of successful atomic density representations.

physics.chem-ph↗

arXiv2023

Vibrational strong coupling in liquid water from cavity molecular dynamics

We assess the cavity molecular dynamics method for the calculation of vibrational polariton spectra, using liquid water as a specific example. We begin by disputing a recent suggestion that nuclear quantum effects may lead to a broadening of polariton bands, finding instead that they merely result in anharmonic red shifts in the polariton frequencies. We go on to show that our simulated cavity spectra can be reproduced to graphical accuracy with a harmonic model that uses just the cavity-free spectrum and the geometry of the cavity as input. We end by showing that this harmonic model can be combined with the experimental cavity-free spectrum to give results in good agreement with optical cavity measurements. Since the input to our harmonic model is equivalent to the input to the transfer matrix method of applied optics, we conclude that cavity molecular dynamics cannot provide any more insight into the effect of vibrational strong coupling on the absorption spectrum than this transfer matrix method, which is already widely used by experimentalists to corroborate their cavity results.

physics.chem-ph↗

arXiv2021

Fast quasi-centroid molecular dynamics

We describe a fast implementation of the quasi-centroid molecular dynamics (QCMD) method in which the quasi-centroid potential of mean force is approximated as a separable correction to the classical interaction potential. This correction is obtained by first calculating quasi-centroid radial and angular distribution functions in a short path integral molecular dynamics simulation, and then using iterative Boltzmann inversion to obtain an effective classical potential that reproduces these distribution functions in a classical NVT simulation. We illustrate this approach with example applications to the vibrational spectra of gas phase molecules, obtaining excellent agreement with QCMD reference calculations for water and ammonia and good agreement with the quantum mechanical vibrational spectrum of methane.

physics.chem-ph↗

arXiv2021

Spin relaxation in radical pairs from the stochastic Schrödinger equation

We show that the stochastic Schrödinger equation (SSE) provides an ideal way to simulate the quantum mechanical spin dynamics of radical pairs. Electron spin relaxation effects arising from fluctuations in the spin Hamiltonian are straightforward to include in this approach, and their treatment can be combined with a highly efficient stochastic evaluation of the trace over nuclear spin states that is required to compute experimental observables. These features are illustrated in example applications to a flavin-tryptophan radical pair of interest in avian magnetoreception, and to a problem involving spin-selective radical pair recombination along a molecular wire. In the first of these examples, the SSE is shown to be both more efficient and more widely applicable than a recent stochastic implementation of the Lindblad equation, which only provides a valid treatment of relaxation in the extreme-narrowing limit. In the second, the exact SSE results are used to assess the accuracy of a recently-proposed combination of Nakajima-Zwanzig theory for the spin relaxation and Schulten-Wolynes theory for the spin dynamics, which is applicable to radical pairs with many more nuclear spins. An appendix analyses the efficiency of trace sampling in some detail, highlighting the particular advantages of sampling with SU(N) coherent states.

quant-ph↗

arXiv2020

An improved path-integral method for golden-rule rates

We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunnelling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang and Richardson. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and coworkers. We then study a multi-dimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretisation of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime, without the need for the analytic continuation required by Wolynes theory.

physics.chem-ph↗

arXiv2020

Confirming the role of nuclear tunnelling in aqueous ferrous-ferric electron transfer

We revisit the well-known aqueous ferrous-ferric electron transfer reaction in order to address recent suggestions that nuclear tunnelling can lead to significant deviation from the linear response assumption inherent in the Marcus picture of electron transfer. A recent study of this reaction by Richardson and coworkers has found a large difference between their new path-integral method, GR-QTST, and the saddle point approximation of Wolynes (Wolynes theory). They suggested that this difference could be attributed to the existence of multiple tunnelling pathways, leading Wolynes theory to significantly overestimate the rate. This was used to argue that the linear response assumptions of Marcus theory may break down for liquid systems when tunnelling is important. If true, this would imply that the commonly used method for studying such systems, where the problem is mapped onto a spin-boson model, is invalid. However, we have recently shown that size inconsistency in GR-QTST can lead to poor predictions of the rate in systems with many degrees of freedom. We have also suggested an improved method, the path-integral linear golden-rule (LGR) approximation, which fixes this problem. Here we demonstrate that the GR-QTST results for ferrous-ferric electron transfer are indeed dominated by its size consistency error. Furthermore, by comparing the LGR and Wolynes theory results, we confirm the established picture of nuclear tunnelling in this system. Finally, by comparing our path-integral results to those obtained by mapping onto the spin-boson model, we reassess the importance of anharmonic effects and the accuracy of this commonly used mapping approach.

physics.chem-ph↗

arXiv2020

A general non-adiabatic quantum instanton approximation

We present a general quantum instanton approach to calculating reaction rates for systems with two electronic states and arbitrary values of the electronic coupling. This new approach, which we call the non-adiabatic quantum instanton (NAQI) approximation, reduces to Wolynes theory in the golden rule limit and to a recently proposed projected quantum instanton (PQI) method in the adiabatic limit. As in both of these earlier theories, the NAQI approach is based on making a saddle point approximation to the time integral of a reactive flux autocorrelation function, although with a generalised definition of the projection operator onto the product states. We illustrate the accuracy of the approach by comparison with exact rates for one dimensional scattering problems and discuss its applicability to more complex reactions.

physics.chem-ph↗

arXiv2020

Quantum mechanical spin dynamics of a molecular magnetoreceptor

Radical pair recombination reactions are known to be sensitive to extremely weak magnetic fields, and can therefore be said to function as molecular magnetoreceptors. The classic example is a carotenoid-porphyrin-fullerene (C+PF-) radical pair that has been shown to provide a "proof-of-principle" for the operation of a chemical compass [K. Maeda et al., Nature 453, 387 (2008)]. Previous simulations of this radical pair have employed semiclassical approximations, which are routinely applicable to its 47 coupled electronic and nuclear spins. However, calculating the exact quantum mechanical spin dynamics presents a significant challenge, and has not been possible before now. Here we use a recently developed method to perform numerically converged simulations of the C+PF- quantum mechanical spin dynamics, including all coupled spins. Comparison of these quantum mechanical simulations with various semiclassical approximations reveals that, while it is not perfect, the best semiclassical approximation does capture essentially all of the relevant physics in this problem.

physics.chem-ph↗