In this work, we present a generalization of the quantum trajectory surface hopping (QTSH) to multiple states and its implementation in the Libra package for nonadiabatic dynamics. In lieu of the ad hoc velocity rescaling used in many trajectory-based surface hopping approaches, QTSH utilizes quantum forces to evolve nuclear degrees of freedom continuously. It also lifts the unphysical constraint of enforcing the total energy conservation at the individual trajectory level and rather conserves the total energy at the trajectory ensemble level. Leveraging our new implementation of the multistate QTSH, we perform a comparative analysis of this method with the conventional fewest switches surface hopping approach. We combine the QTSH and decoherence corrections based on the simplified decay of mixing (SDM) and exact factorization (XF), leading to the QTSH-SDM and QTSH-XF schemes. Using the Holstein, superexchange, and phenol model Hamiltonians, we assess the relative accuracy of the resulting combined schemes in reproducing branching ratios, population, and coherence dynamics for a broad range of initial conditions. We observe that the decoherence correction in QTSH is crucial to improve energy conservation as well as the internal consistency between the population from the quantum probability and active state.

Two-dimensional materials provide a rich platform demonstrating quantum effects, and the process of electron-hole recombination occurring in them has significant applications in the fields of the photocatalytic and optoelectronic community. Here, we present nonadiabatic coupling-induced quantum coherence and quantum beats in Al-doped blue phosphorene. The work improves our understanding and utilization of nonadiabatic coupling in low-dimensional materials from a new perspective. In addition, our investigations provide meaningful guidance for manipulating quantum coherence in low-dimensional materials and promoting their novel optoelectronic properties.

In this paper, we investigate the time evolution of quantum coherence-the off-diagonal elements of the density matrix of a multistate quantum system-from the perspective of the Wigner-Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit-an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable.

The fewest switches surface hopping (FSSH) method proposed by Tully in 1990 [Tully, J. Chem. Phys. 93, 1061 (1990)]-along with its many later variations-forms the basis for most practical simulations of molecular dynamics with electronic transitions in realistic systems. Despite its popularity, a rigorous formal derivation of the algorithm has yet to be achieved. In this paper, we derive the energy-conserving momentum jumps employed by FSSH from the perspective of quantum trajectory surface hopping (QTSH) [Martens, J. Phys. Chem. A 123, 1110 (2019)]. In the limit of localized nonadiabatic transitions, simple mathematical and physical arguments allow the FSSH algorithm to be derived from first principles. For general processes, the quantum forces characterizing the QTSH method provide accurate results for nonadiabatic dynamics with rigorous energy conservation, at the ensemble level, within the consistency of the underlying stochastic surface hopping without resorting to the artificial momentum rescaling of FSSH.

The vibrational predissociation of van der Waals complexes has been the object of study using a wide range of theoretical and experimental methods, producing a large number of results. We focus here on the ArBr _2 ( v=16,… ,25 ) system. For its study, we employ two important theoretical methods: the trajectory surface hopping (TSH) and the quasiclassical trajectory method (QCTM). In the first case, the dynamics of the system are reproduced on a potential energy surface (PES) corresponding to quantum molecular vibrational states. The possibility of hopping to other vibrational surfaces is also included, which can then lead to van der Waals bond dissociation. On the other hand, the second case consists of propagating the dynamics over a single potential energy surface. We incorporate the kinetic mechanism into the TSH method for better comparison of the evolution of the complex. Both methods allow us to study the dynamical behavior of the ArBr _2 as well as several observables. We compute the lifetime, exit channel, rotational energy, and maximum angular momentum ( j_max ) of Br _2 . We compare our results with previous experimental and theoretical work and also report new results for cases that have not previously been considered. Graphical abstract

The vibrational predissociation of van der Waals complexes has been the object of study using a wide range of theoretical and experimental methods, producing a large number of results. We focus here on the ArBr $$_2$$ ( $$v=16,\ldots ,25$$ ) system. For its study, we employ two important theoretical methods: the trajectory surface hopping (TSH) and the quasiclassical trajectory method (QCTM). In the first case, the dynamics of the system are reproduced on a potential energy surface (PES) corresponding to quantum molecular vibrational states. The possibility of hopping to other vibrational surfaces is also included, which can then lead to van der Waals bond dissociation. On the other hand, the second case consists of propagating the dynamics over a single potential energy surface. We incorporate the kinetic mechanism into the TSH method for better comparison of the evolution of the complex. Both methods allow us to study the dynamical behavior of the ArBr $$_2$$ as well as several observables. We compute the lifetime, exit channel, rotational energy, and maximum angular momentum ( $$j_{max}$$ ) of Br $$_2$$ . We compare our results with previous experimental and theoretical work and also report new results for cases that have not previously been considered.

Yair Litman opened discussion of the paper by Stuart C. Althorpe: Did you try to use a linear model for the dipole in the gas-phase water simulations to address the importance of the electrical anharmonicity? Raz L. Benson responded: As stated in the Faraday Discussions paper (DO

The vibrational predissociation of NeBr2 has been studied using a variety of theoretical and experimental methods, producing a large number of results. It is therefore a useful system for comparing different theoretical methods. Here, we apply the trajectory surface hopping (TSH) method that consists of propagating the dynamics of the system on a potential energy surface (PES) corresponding to quantum molecular vibrational states with possibility of hopping towards other surfaces until the van der Waals bond dissociates. This allows quantum vibrational effects to be added to a classical dynamics approach. We have also incorporated the kinetic mechanism for a better compression of the evolution of the complex. The novelty of this work is that it allows us to incorporate all the surfaces for (v=16,17,…,29) into the dynamics of the system. The calculated lifetimes are similar to those previously reported experimentally and theoretically. The rotational distribution, the rotational energy and jmax are in agreement with other works, providing new information for this complex.

The first page of this article is displayed as the abstract.

In this paper, we analyze the detailed quantum-classical behavior of two alternative approaches to simulating molecular dynamics with electronic transitions: the popular fewest switches surface hopping (FSSH) method, introduced by Tully in 1990 [Tully, J. Chem. Phys., 1990, 93, 1061] and our recently developed quantum trajectory surface hopping (QTSH) method [Martens, J. Phys. Chem. A, 2019, 123, 1110]. Both approaches employ an independent ensemble of trajectories that undergo stochastic transitions between electronic surfaces. The methods differ in their treatment of energy conservation, with FSSH imposing conservation of the classical kinetic plus potential energy by rescaling the classical momentum when a surface hop occurs while QTSH incorporates a quantum force throughout the dynamics which leads naturally to the conservation of the full quantum-classical energy. We investigate the population transfer and energy budget of the surface hopping methods for several simple model systems and compare with exact quantum results. In addition, the detailed dynamics of the trajectory ensembles in phase space are compared with the quantum evolution in the Wigner representation. Conclusions are drawn.

Yair Litman opened discussion of the paper by Soumya Ghosh: Could you elaborate on why the SH-RP-iso simulations give rates that are virtually temperature independent even approaching 300 K? Soumya Ghosh responded: We discussed this interesting aspect briefly in our paper (DOI: 1

ADVERTISEMENT RETURN TO ISSUESpecial Issue Prefac...Special Issue PrefaceNEXTTribute to William P. ReinhardtCraig C. MartensCraig C. MartensUniversity of California, IrvineMore by Craig C. Martenshttp://orcid.org/0000-0002-2350-4346 and David J. MasielloDavid J. MasielloUniversity of WashingtonMore by David J. Masiellohttp://orcid.org/0000-0002-1187-0920Cite this: J. Phys. Chem. A 2019, 123, 17, 3615–3616Publication Date (Web):May 2, 2019Publication History Published online2 May 2019Published inissue 2 May 2019https://pubs.acs.org/doi/10.1021/acs.jpca.9b01985https://doi.org/10.1021/acs.jpca.9b01985introductionACS PublicationsCopyright © 2019 American Chemical Society. This publication is available under these Terms of Use. Request reuse permissions This publication is free to access through this site. Learn MoreArticle Views954Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail PDF (813 KB) Get e-AlertscloseSupporting Info (1)»Supporting Information Supporting Information SUBJECTS:Anions,Energy transfer,Mathematical methods,Students Get e-Alerts

We describe a new method for simulating nonadiabatic dynamics using stochastic trajectories. The method, which we call quantum trajectory surface hopping (QTSH), is a variant of the popular fewest-switches surface-hopping (FSSH) approach, but with important differences. We briefly review and significantly extend our recently described consensus surface-hopping (CSH) formalism, which captures quantum effects such as coherence and decoherence via a collective representation of the quantum dynamics at the ensemble level. Using well-controlled further approximations, we derive an independent trajectory limit of CSH that recovers the FSSH stochastic algorithm but rejects the ad hoc momentum rescaling of FSSH in favor of quantum forces that couple classical and quantum degrees of freedom and lead to nonclassical trajectory dynamics. The approach is well-defined in both the diabatic and adiabatic representations. In the adiabatic representation, the classical dynamics are modified by a quantum-state-dependent vector potential, introducing geometric phase effects into the dynamics of multidimensional systems. Unlike FSSH, our method obeys energy conservation without any artificial momentum rescaling, eliminating undesirable features of the former such as forbidden hops and breakdown of the internal consistency of quantum and ensemble-based state probabilities. Corrections emerge naturally in the formalism that allow approximate incorporation of decoherence without the computational expense of the full CSH approach. The method is tested on several model systems. QTSH provides a surface-hopping methodology that has a rigorous foundation and broader applicability than FSSH while retaining the low computational cost of an independent trajectory framework.

Nanopores have become a subject of interest in the scientific community due to their potential uses in nanometer-scale laboratory and research applications, including infectious disease diagnostics and DNA sequencing. Additionally, they display behavioral similarity to molecular and cellular scale physiological processes. Recent advances in information theory have made it possible to probe the information dynamics of nonlinear stochastic dynamical systems, such as autonomously fluctuating nanopore systems, which has enhanced our understanding of the physical systems they model. We present the results of local (LER) and specific entropy rate (SER) computations from a simulation study of an autonomously fluctuating nanopore system. We learn that both metrics show increases that correspond to fluctuations in the nanopore current, indicating fundamental changes in information generation surrounding these fluctuations.

In this paper we present a trajectory-based formulation of entanglement dynamics by employing the Wigner function. The linear entropy of a single trajectory is derived based on the trajectory evolution of the Wigner function. The entanglement dynamics with a separable Gaussian initial state is investigated using different values of Planck's constant (h) over bar in the evolution of the trajectories, while quantum-classical correspondence in entanglement dynamics is investigated. In addition, we show why chaos can increase entanglement rapidly through analytical results and physical pictures of the underlying dynamics in phase space.

We present a new stochastic surface hopping method for modeling molecular dynamics with electronic transitions. The approach, consensus surface hopping (CSH), is a numerical framework for solving the semiclassical limit Liouville equation describing nuclear dynamics on coupled electronic surfaces using ensembles of trajectories. In contrast to existing techniques based on propagating independent classical trajectories that undergo stochastic hops between the electronic states, the present method determines the probabilities of transition of each trajectory collectively with input from the entire ensemble. The full coherent dynamics of the coupled system arise naturally at the ensemble level and ad hoc corrections, such as momentum rescaling to impose strict trajectory energy conservation and artificial decoherence to avoid the overcoherence of the quantum states associated with independent trajectories, are avoided.

In this paper, we revisit the semiclassical Liouville approach to describing molecular dynamics with electronic transitions using classical trajectories. Key features of the formalism are highlighted. The locality in phase space and presence of nonclassical terms in the generalized Liouville equations are emphasized and discussed in light of trajectory surface hopping methodology. The representation dependence of the coupled semiclassical Liouville equations in the diabatic and adiabatic bases are discussed and new results for the transformation theory of the Wigner functions representing the corresponding density matrix elements given. We show that the diagonal energies of the state populations are not conserved during electronic transitions, as energy is stored in the electronic coherence. We discuss the implications of this observation for the validity of imposing strict energy conservation in trajectory based methods for simulating nonadiabatic processes.

In this paper, we describe a new and fully coherent stochastic surface hopping method for simulating mixed quantum-classical systems. We illustrate the approach on the simple but unforgiving problem of quantum evolution of a two-state quantum system in the limit of unperturbed pure state dynamics and for dissipative evolution in the presence of both stationary and nonstationary random environments. We formulate our approach in the Liouville representation and describe the density matrix elements by ensembles of trajectories. Population dynamics are represented by stochastic surface hops for trajectories representing diagonal density matrix elements. These are combined with an unconventional coherent stochastic hopping algorithm for trajectories representing off-diagonal quantum coherences. The latter generalizes the binary (0,1) "probability" of a trajectory to be associated with a given state to allow integers that can be negative or greater than unity in magnitude. Unlike existing surface hopping methods, the dynamics of the ensembles are fully entangled, correctly capturing the coherent and nonlocal structure of quantum mechanics.

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.