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The assertion by the troubled teacher Patrick Doyle – “I just tell the bloody truth, as I see it” (p. 112) – in James Kelman’s novel A Disaffection goes to the heart of Kelman’s own aesthetic of showing things as they are. However, the qualifying clause – “as I see it” – also suggests that truth is not evidentially absolute and immediate but provisional or situated. Of course the very concept of truth would seem to require of itself a totalised fulfilment of its own promise. That is, truth sh...

We show how linear vibronic spectra in molecular systems can be simulated efficiently using first-principles approaches without relying on the explicit use of multiple Born-Oppenheimer potential energy surfaces. We demonstrate and analyze the performance of mean-field and beyond-mean-field dynamics techniques for the H2 molecule in one dimension, in the later case capturing the vibronic structure quite accurately, including quantum Franck-Condon effects. In a practical application of this methodology we simulate the absorption spectrum of benzene in full dimensionality using time-dependent density functional theory at the multitrajectory Ehrenfest level, finding good qualitative agreement with experiment and significant spectral reweighting compared to commonly used single-trajectory Ehrenfest dynamics. These results form the foundation for nonlinear spectral calculations and show promise for future application in capturing phenomena associated with vibronic coupling in more complex molecular and potentially condensed phase systems This work was supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence Advanced Imaging of Matter (AIM), JSPS KAKENHI Grant Number 20K14382, Grupos Consolidados (IT1249-19), and SFB925. The Flatiron Institute is a division of the Simons Foundation

Quasi-classical mapping Hamiltonian methods have recently emerged as a promising approach for simulating electronically nonadiabatic molecular dynamics. The classical-like dynamics of the overall system within these methods makes them computationally feasible, and they can be derived based on well-defined semiclassical approximations. However, the existence of a variety of different quasi-classical mapping Hamiltonian methods necessitates a systematic comparison of their respective advantages and limitations. Such a benchmark comparison is presented in this paper. The approaches compared include the Ehrenfest method, the symmetrical quasi-classical (SQC) method, and five variations of the linearized semiclassical (LSC) method, three of which employ a modified identity operator. The comparison is based on a number of popular nonadiabatic model systems; the spin-boson model, a Frenkel biexciton model, and Tully’s scattering models 1 and 2. The relative accuracy of the different methods is tested by comparing with quantum-mechanically exact results for the dynamics of the electronic populations and coherences. We find that LSC with the modified identity operator typically performs better than the Ehrenfest and standard LSC approaches. In comparison to SQC, these modified methods appear to be slightly more accurate for condensed phase problems, but for scattering models there is little distinction between them., Journal of Chemical Theory and Computation, 16 (5), ISSN:1549-9618, ISSN:1549-9626

The formalism of the generalized quantum master equation (GQME) is an effective tool to simultaneously increase the accuracy and the efficiency of quasiclassical trajectory methods in the simulation of nonadiabatic quantum dynamics. The GQME expresses correlation functions in terms of a non-Markovian equation of motion, involving memory kernels that are typically fast-decaying and can therefore be computed by short-time quasiclassical trajectories. In this paper, we study the approximate solution of the GQME, obtained by calculating the kernels with two methods: Ehrenfest mean-field theory and spin-mapping. We test the approaches on a range of spin–boson models with increasing energy bias between the two electronic levels and place a particular focus on the long-time limits of the populations. We find that the accuracy of the predictions of the GQME depends strongly on the specific technique used to calculate the kernels. In particular, spin-mapping outperforms Ehrenfest for all the systems studied. The problem of unphysical negative electronic populations affecting spin-mapping is resolved by coupling the method with the master equation. Conversely, Ehrenfest in conjunction with the GQME can predict negative populations, despite the fact that the populations calculated from direct dynamics are positive definite., The Journal of Chemical Physics, 157 (23), ISSN:0021-9606, ISSN:1089-7690

[EN] We demonstrate that a conditional wave function theory enables a unified and efficient treatment of the equilibrium structure and nonadiabatic dynamics of correlated electron-ion systems. The conditional decomposition of the many-body wave function formally recasts the full interacting wave function of a closed system as a set of lower-dimensional (conditional) coupled "slices". We formulate a variational wave function ansatz based on a set of conditional wave function slices and demonstrate its accuracy by determining the structural and time-dependent response properties of the hydrogen molecule. We then extend this approach to include time-dependent conditional wave functions and address paradigmatic nonequilibrium processes including strong-field molecular ionization, laser-driven proton transfer, and nuclear quantum effects induced by a conical intersection. This work paves the road for the application of conditional wave function theory in equilibrium and out-of-equilibrium ab initio molecular simulations of finite and extended systems. This work was supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence “CUI: Advanced Imaging of Matter” of the Deutsche Forschungsgemeinschaft (DFG)─EXC 2056─project ID 390715994, Grupos Consolidados (IT1249-19), and the SFB925 “Light induced dynamics and control of correlated quantum systems”. The Flatiron Institute is a division of the Simons Foundation. The authors also acknowledge financial support from the JSPS KAKENHI Grant Number 20K14382, the Spanish Ministerio de Economía y Competitividad, Project Nos. PID2019-109518GB-I00 and CTQ2017-87773-P/AEI/FEDER, the Spanish Structures of Excellence María de Maeztu program through grant MDM-2017-0767, and Generalitat de Catalunya, Project No. 2017 SGR 348.

Recent experimental realizations of strong coupling between optical cavity modes and molecular matter placed inside the cavity have opened exciting new routes for controlling chemical processes. Simulating the cavity-modified dynamics of complex chemical systems calls for the development of accurate, flexible, and cost-effective approximate numerical methods that scale favorably with system size and complexity. In this Letter, we test the ability of quasiclassical mapping Hamiltonian methods to serve this purpose. We simulated the spontaneous emission dynamics of an atom confined to a microcavity via five different variations of the linearized semiclassical (LSC) method. Our main finding is that recently proposed LSC-based methods which use a modified form of the identity operator are reasonably accurate and perform significantly better than the Ehrenfest and standard LSC methods, without significantly increasing computational costs. These methods are therefore highly promising as a general purpose tool for simulating cavity-modified dynamics of complex chemical systems.

Heparin-induced thrombocytopenia (HIT) poses a risk of death secondary to thrombotic complications.Treatment options are limited for patients with poor IV access, as contemporary options are restricted to parenteral agents before switching to oral vitamin k antagonists. A literature review was conducted to examine the effectiveness of direct oral anticoagulants (DOACs) in the primary treatment of HIT. High quality evidence is scarce surrounding the use of DOACs for this indication, while past reviews have not critically appraised the evidence. Additionally, the most recent study from 2017 investigating the use of DOACs for this indication has not been reported in past literature reviews.The Cochrane Library, Embase, PubMed, Google Scholar and ClinicalTrials.gov were searched to identify and critically appraise the best available evidence. Salient literature demonstrates that DOACs are effective at raising platelet count to baseline after seven days, on average.Thrombosis and major bleeding are rarely observed when DOACs are used as primary therapy. While large scale studies are needed, patients with HIT that have poor IV access may benefit from the ease of administration, rapid onset of action and lack of routine monitoring associated with DOAC therapy.

Mean field theory is applied to nonequilibrium thermal energy transport in a model molecular junction. An approximation to the total time-dependent heat current in the junction is constructed using an ensemble of Ehrenfest trajectories, and the average heat current in the steady state is obtained. The accuracy of this treatment is verified through benchmark comparisons with exact quantum mechanical results, and various approximate quantum transport theories, for the nonequilibrium spin-boson model. The performance of the multi-trajectory Ehrenfest approach is found to be quite robust, displaying good accuracy in intermediate cases that remain elusive to many perturbative approximations, and in the strong coupling limit where many methods break down. Thus, mean field theory and related trajectory-based approximate quantum dynamics methods emerge as a promising toolkit for the study of transport properties in nanoscale systems.

The mapping approach addresses the mismatch between the continuous nuclear phase space and discrete electronic states by creating an extended, fully continuous phase space using a set of harmonic oscillators to encode the populations and coherences of the electronic states. Existing quasiclassical dynamics methods based on mapping, such as the linearised semiclassical initial value representation (LSC-IVR) and Poisson bracket mapping equation (PBME) approaches, have been shown to fail in predicting the correct relaxation of electronic-state populations following an initial excitation. Here we generalise our recently published modification to the standard quasiclassical approximation for simulating quantum correlation functions. We show that the electronic-state population operator in any system can be exactly rewritten as a sum of a traceless operator and the identity operator. We show that by treating the latter at a quantum level instead of using the mapping approach, the accuracy of traditional quasiclassical dynamics methods can be drastically improved, without changes to their underlying equations of motion. We demonstrate this approach for the seven-state Frenkel-exciton model of the Fenna-Matthews-Olson light harvesting complex, showing that our modification significantly improves the accuracy of traditional mapping approaches when compared to numerically exact quantum results.

Methods derived from the generalized quantum master equation (GQME) framework have provided the basis for elucidating energy and charge transfer in systems ranging from molecular solids to photosynthetic complexes. Recently, the non-perturbative combination of the GQME with quantum-classical methods has resulted in approaches whose accuracy and efficiency exceed those of the original quantum-classical schemes while offering significant accuracy improvements over perturbative expansions of the GQME. Here we show that, while the non-Markovian memory kernel required to propagate the GQME scales quartically with the number of subsystem states, the number of trajectories required scales at most quadratically when using quantum-classical methods to construct the kernel. We then present an algorithm that allows further acceleration of the quantum-classical GQME by providing a way to selectively sample the kernel matrix elements that are most important to the process of interest. We demonstrate the utility of these advances by applying the combination of Ehrenfest mean field theory with the GQME (MF-GQME) to models of the Fenna-Matthews-Olson (FMO) complex and the light harvesting complex II (LHCII), with 7 and 14 states, respectively. This allows us to show that MF-GQME is able to accurately capture all the relevant dynamical time-scales in LHCII: the initial nonequilibrium population transfer on the femtosecond time-scale, the steady state-type trapping on the picosecond time-scale, and the long time population relaxation. Remarkably, all of these physical effects spanning tens of picoseconds can be encoded in a memory kernel that decays after only $\sim$65 fs., Comment: 17 page manuscript (7 figures), 3 page supplementary material; updated to published version of manuscript

In organic photovoltaic (OPV) systems, exciton dissociation and ultrafast charge separation at donor-acceptor heterojunctions both play a key role in controlling the efficiency of the conversion of excitation energy into free charge carriers. In this work, nonadiabatic dynamics simulations based on the quantum-classical Liouville equation, are employed to study the real-time dynamics of exciton dissociation and charge separation at a model donor-acceptor interface. Benchmark comparisons for a variety of low dimensional donor-acceptor chain models are performed to assess the accuracy of the quantum classical dynamics technique referred to as the forward-backward trajectory solution (FBTS). Although not always quantitative, the FBTS approach offers a reasonable balance between accuracy and computational cost. The short-time dynamics of exciton dissociation in related higher-dimensional lattice models for the interface are also investigated to assess the effect of the dimensionality on the first steps in the mechanism of charge carrier generation.

We describe vacuum fluctuations and photon-field correlations in interacting quantum mechanical light-matter systems, by generalizing the application of mixed quantum-classical dynamics techniques. We employ the multi-trajectory implementation of Ehrenfest mean field theory, traditionally developed for electron-nuclear problems, to simulate the spontaneous emission of radiation in a model quantum electrodynamical cavity-bound atomic system. We investigate the performance of this approach in capturing the dynamics of spontaneous emission from the perspective of both the atomic system and the cavity photon field, through a detailed comparison with exact benchmark quantum mechanical observables and correlation functions. By properly accounting for the quantum statistics of the vacuum field, while using mixed quantum-classical (mean field) trajectories to describe the evolution, we identify a surprisingly accurate and promising route towards describing quantum effects in realistic correlated light-matter systems.

We present an ab initio algorithm for quantum dynamics simulations that reformulates the traditional ``curse of dimensionality'' that plagues all state-of-the-art techniques for solving the time-dependent Schr\"odinger equation. Using a stochastic wave-function ansatz that is based on a set of interacting single-particle conditional wave functions, we show that the difficulty of the problem becomes dominated by the number of trajectories needed to describe the process, rather than simply the number of degrees of freedom involved. This highly parallelizable technique achieves quantitative accuracy for situations in which mean-field theory drastically fails to capture qualitative aspects of the dynamics, such as quantum decoherence or the reduced nuclear probability density, using orders of magnitude fewer trajectories than a mean-field simulation. We illustrate the performance of this method for two fundamental nonequilibrium processes: a photoexcited proton-coupled electron transfer problem, and nonequilibrium dynamics in a cavity bound electron-photon system in the ultrastrong-coupling regime.

This article seeks to defend James Connolly from attacks on both the Left and Right, particularly the charge that his legacy is nationalist delusion and fanaticism. The article argues that Connolly’s politics and his engagement with Irish cultural politics demonstrate his commitment to human equality as both a right, but also a principle of human intelligence. The article addresses Connolly’s status as a working-class intellectual with reference to how he challenges conventional hierarchies between the philosophers of Marxism and the proletarians who are the object of those deliberations. The article argues that from Connolly’s thought and activism an anti-colonial Marxism emerges which might help explain the neo-imperialist world we find ourselves in today and provide a critique lacking in the collapsed teleological versions of orthodox Marxism. The relations between his Marxism and nationalism are explored, as are his play Under Which Flag? his poetry and songs.

Simulating the nonadiabatic dynamics of condensed-phase systems continues to pose a significant challenge for quantum dynamics methods. Approaches based on sampling classical trajectories within the mapping formalism, such as the linearized semiclassical initial value representation (LSC-IVR), can be used to approximate quantum correlation functions in dissipative environments. Such semiclassical methods however commonly fail in quantitatively predicting the electronic-state populations in the long-time limit. Here we present a suggestion to minimize this difficulty by splitting the problem into two parts, one of which involves the identity and treating this operator by quantum-mechanical principles rather than with classical approximations. This strategy is applied to numerical simulations of spin-boson model systems, showing its potential to drastically improve the performance of LSC-IVR and related methods with no change in the equations of motion or the algorithm in general, but rather by simply using different functional forms of the observables., The Journal of Chemical Physics, 150 (7), ISSN:0021-9606, ISSN:1089-7690

We introduce a simple ansatz for the wave function of a many-body system based on coupled forward and backward propagating semiclassical trajectories. This method is primarily aimed at, but not limited to, treating nonequilibrium dynamics in electron-phonon systems. The time evolution of the system is obtained from the Euler-Lagrange variational principle, and we show that this ansatz yields Ehrenfest mean-field theory in the limit that the forward and backward trajectories are orthogonal, and in the limit that they coalesce. We investigate accuracy and performance of this method by simulating electronic relaxation in the spin-boson model and the Holstein model. Although this method involves only pairs of semiclassical trajectories, it shows a substantial improvement over mean-field theory, capturing quantum coherence of nuclear dynamics as well as electron-nuclear correlations. This improvement is particularly evident in nonadiabatic systems, where the accuracy of this coupled trajectory method extends well beyond the perturbative electron-phonon coupling regime. This approach thus provides an attractive route forward to the ab initio description of relaxation processes, such as thermalization, in condensed phase systems.

The development of methods that can efficiently and accurately treat nonadiabatic dynamics in quantum systems coupled to arbitrary atomistic environments remains a significant challenge in problems ranging from exciton transport in photovoltaic materials to electron and proton transfer in catalysis. Here we show that our recently introduced MF-GQME approach, which combines Ehrenfest mean field theory with the generalized quantum master equation framework, is able to yield quantitative accuracy over a wide range of charge-transfer regimes in fully atomistic environments. This is accompanied by computational speed-ups of up to 3 orders of magnitude over a direct application of Ehrenfest theory. This development offers the opportunity to efficiently investigate the atomistic details of nonadiabatic quantum relaxation processes in regimes where obtaining accurate results has previously been elusive.

We benchmark a selection of semiclassical and perturbative dynamics techniques by investigating the correlated evolution of a cavity-bound atomic system to assess their applicability to study problems involving strong light-matter interactions in quantum cavities. The model system of interest features spontaneous emission, interference, and strong coupling behaviour, and necessitates the consideration of vacuum fluctuations and correlated light-matter dynamics. We compare a selection of approximate dynamics approaches including fewest switches surface hopping, multi-trajectory Ehrenfest dynamics, linearized semiclasical dynamics, and partially linearized semiclassical dynamics. Furthermore, investigating self-consistent perturbative methods, we apply the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the second Born approximation. With the exception of fewest switches surface hopping, all methods provide a reasonable level of accuracy for the correlated light-matter dynamics, with most methods lacking the capacity to fully capture interference effects., Comment: 12 pages , 11 figures

Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach seems to offer no advantage over a direct evaluation of the property of interest. Here we provide a more detailed understanding of the conditions under which these methods will offer benefits. In particular, we derive exact expressions for the memory kernel for systems both in and out of equilibrium, and show the conditions under which these expressions will be guaranteed to return a result identical to that obtained from direct simulation. We also show the conditions which approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These exact analytical results thus provide new insights as to when proceeding via the GQME approach can improve the accuracy or efficiency of simulations., 5 pages, 0 figures

The Fenna−Matthews−Olsen (FMO) complex has recently become a paradigmatic model system in terms of understanding the long-lived electronic quantum coherence that has been experimentally observed in photosynthetic systems. In this article we investigate the quantum dynamics of an FMO model within a mixed quantum-classical dynamics approach known as the Poisson bracket mapping equation (PBME), and explore the consequences of adopting this approximate description by simulating population transfer and electronic coherence. The results obtained via the Poisson bracket mapping formalism are explicitly compared with a selection of recent results on the FMO complex. The PBME is shown to be in excellent agreement with benchmark computational results at physiological temperature, and thus provides a computationally efficient and physically consistent algorithm that may be easily integrated in all-atom molecular dynamics simulations.

In this article we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times., 10 pages, 6 figures

A quantum mechanical definition of molecular size and shape is formulated from the electronic second moment of the Hartree-Fock wave function. The shape tensor is defined to be invariant with respect to the origin. The geometric average of the eigenvalues of the tensor correlates very well with van der Waals and Bragg-Slater radii. There is also a close linear relationship between this definition of molecular size and molecular volumes determined computationally using isodensity contours. Furthermore, this definition of molecular size is effective in predicting the steric effects of substituents, as predicted by existing methods, such as the modified Taft Ee(s), P-values, and n-values.

Although photosynthetic pigment-protein complexes are in noisy environments, recent experimental and theoretical results indicate that their excitation energy transfer (EET) can exhibit coherent characteristics for over hundreds of femtoseconds. Despite the almost universal observations of the coherence to some degree, questions still remain regarding the detailed role of the protein and the extent of high-temperature coherence. Here we adopt a theoretical method that incorporates an all-atom description of the photosynthetic complex within a semiclassical framework in order to study EET in the Fenna-Matthews-Olson complex. We observe that the vibrational modes of the chromophore tend to diminish the coherence at the ensemble level, yet much longer-lived coherences may be observed at the single-complex level. We also observe that coherent oscillations in the site populations also commence within tens of femtoseconds even when the system is initially prepared in a non-oscillatory stationary state. We show that the protein acts to maintain the electronic couplings among the system of embedded chromophores. We also investigate the extent to which the protein's electrostatic modulation that disperses the chromophore electronic energies may affect the coherence lifetime. Further, we observe that even though mutation-induced disruptions in the protein structure may change the coupling pattern, a relatively strong level of coupling and associated coherence in the dynamics still remain. Finally, we demonstrate that thermal fluctuations in the chromophore couplings induce some redundancy in the coherent energy-transfer pathway. Our results indicate that a description of both chromophore coupling strengths and their fluctuations is crucial to better understand coherent EET processes in photosynthetic systems.

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems., 4 figures

In this chapter we discuss approaches to solving quantum dynamics in the condensed phase based on the quantum-classical Liouville method. Several representations of the quantum-classical Liouville equation (QCLE) of motion have been investigated and subsequently simulated. We discuss the benefits and limitations of these approaches. By making further approximations to the QCLE, we show that standard approaches to this problem, i.e., mean-field and surface-hopping methods, can be derived. The computation of transport coeffcients, such as chemical rate constants, represent an important class of problems where the QCL method is applicable. We present a general quantum-classical expression for a time-dependent transport coeffcient which incorporates the full system’s initial quantum equilibrium structure. As an example of the formalism, the computation of a reaction rate coeffcient for a simple reactive model is presented. These results are compared to illuminate the similarities and differences between various approaches discussed in this chapter.