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We have extended the semiclassical-based electron force-field simulation by introducing field–electron interaction to enable us to describe linear and nonlinear electronic excitation dynamics of a condensed matter system with low computational cost. To verify the simulation method, as a first step, numerical examples of interaction dynamics of simple systems (H atom, SiH4 molecule, and Si crystalline solid) with applied short electric field pulse as well as the obtained absorbed energies by the one- and two-photon excitations have been reported along with comparison with quantum dynamics calculations as reference. [ABSTRACT FROM AUTHOR]

In this Communication, we demonstrate that a deep artificial neural network based on a transformer architecture with self-attention layers can predict the long-time population dynamics of a quantum system coupled to a dissipative environment provided that the short-time population dynamics of the system is known. The transformer neural network model developed in this work predicts the long-time dynamics of spin-boson model efficiently and very accurately across different regimes, from weak system–bath coupling to strong coupling non-Markovian regimes. Our model is more accurate than classical forecasting models, such as recurrent neural networks, and is comparable to the state-of-the-art models for simulating the dynamics of quantum dissipative systems based on kernel ridge regression. [ABSTRACT FROM AUTHOR]

Modeling the dynamics of a quantum system coupled to a dissipative environment becomes particularly challenging when the system's dimensionality is too high to permit the computation of its eigenstates. This problem is addressed by introducing an eigenstate-free formalism, where the open quantum system is represented as a mixture of high-dimensional, time-dependent wave packets governed by coupled Schrödinger equations, while the environment is described by a multi-component quantum master equation. An efficient computational implementation of this formalism is presented, employing a variational mixed Gaussian/multiconfigurational time-dependent Hartree (G-MCTDH) ansatz for the wave packets and propagating the environment dynamics via hierarchical equations, truncated at the first or second level of the hierarchy. The effectiveness of the proposed methodology is demonstrated on a 61-dimensional model of phonon-driven vibrational relaxation of an adsorbate. G-MCTDH calculations on 4- and 10-dimensional reduced models, combined with truncated hierarchical equations for the mean fields, nearly quantitatively replicate the full-dimensional quantum dynamical results on vibrational relaxation while significantly reducing the computational time. This approach thus offers a promising quantum dynamical method for modeling complex system–bath interactions, where a large number of degrees of freedom must be explicitly considered. [ABSTRACT FROM AUTHOR]

The generalized quantum master equation (GQME) approach provides a powerful general-purpose framework for simulating the inherently quantum mechanical dynamics of a subset of electronic reduced density matrix elements of interest in complex molecular systems. Previous studies have found that combining the GQME approach with quasiclassical mapping Hamiltonian (QC/MH) methods can dramatically improve the accuracy of electronic populations obtained via those methods. In this paper, we perform a complimentary study of the advantages offered by the GQME approach for simulating the dynamics of electronic coherences, which play a central role in optical spectroscopy, quantum information science, and quantum technology. To this end, we focus on cases where the electronic coherences predicted for the spin-boson benchmark model by direct application of various QC/MH methods are inaccurate. We find that similar to the case of electronic populations, combining the QC/MH methods with the GQME approach can dramatically improve the accuracy of the electronic coherences obtained via those methods. We also provide a comprehensive analysis of how the performance of GQMEs depends on the choice of projection operator and electronic basis and show that the accuracy and feasibility of the GQME approach can benefit from casting the GQME in terms of the eigen-basis of the observable of interest. [ABSTRACT FROM AUTHOR]

The accurate description of the interaction of a quantum system with its environment is a challenging problem ubiquitous across all areas of physics and lies at the foundation of quantum mechanics theory. Here, we pioneer a new strategy to create discrete low-rank models of the system–environment interaction, by exploiting the frequency and time domain information encoded in the fluctuation–dissipation relation connecting the system–bath correlation function and the spectral density. We demonstrate the effectiveness of our methodology by combining it with tensor-network methodologies and simulating the quantum dynamics of complex excitonic systems in a highly structured bosonic environment. The new modeling framework sets the basis for a leap in the analysis of open quantum systems, providing controlled accuracy at significantly reduced computational costs, with benefits in all connected research areas. [ABSTRACT FROM AUTHOR]

Developing numerical exact solvers for open quantum systems is a challenging task due to the non-perturbative and non-Markovian nature when coupling to structured environments. The Feynman–Vernon influence functional approach is a powerful analytical tool to study the dynamics of open quantum systems. Numerical treatments of the influence functional including the quasi-adiabatic propagator technique and the tensor-network-based time-evolving matrix product operator method have proven to be efficient in studying open quantum systems with bosonic environments. However, the numerical implementation of the fermionic path integral suffers from the Grassmann algebra involved. In this work, we present a detailed introduction to the Grassmann time-evolving matrix product operator method for fermionic open quantum systems. In particular, we introduce the concepts of Grassmann tensor, signed matrix product operator, and Grassmann matrix product state to handle the Grassmann path integral. Using the single-orbital Anderson impurity model as an example, we review the numerical benchmarks for structured fermionic environments for real-time nonequilibrium dynamics, real-time and imaginary-time equilibration dynamics, and its application as an impurity solver. These benchmarks show that our method is a robust and promising numerical approach to study strong coupling physics and non-Markovian dynamics. It can also serve as an alternative impurity solver to study strongly correlated quantum matter with dynamical mean-field theory. [ABSTRACT FROM AUTHOR]

Our study is devoted to the thermophysical properties of solid and liquid nickel in the vicinity of the melting point. For this purpose, we use a first-principles calculation method based on quantum molecular dynamics and experimental measurements with a pulse heating technique. We provide experimental and calculated data on thermal expansion, molar enthalpy, sound velocity, resistivity, and normal spectral emissivity and analyze them together with available experimental and reference data on solid and liquid Ni. We confirm experimentally and computationally the strong temperature dependence of Ni density observed in several experiments. Our fusion enthalpy measurements are in good agreement with the recommended literature data, and the calculation predicts a slightly smaller change in enthalpy. The experimental measurements of nickel resistivity in the solid and liquid states agree with previous experimental data that take into account its correction for thermal expansion. At the same time, our calculation of the resistivity in the solid phase shows a systematic shift. For liquid nickel, we report a weak nonlinear temperature dependence of the normal spectral emissivity. Thus, taking advantage of experimental and ab initio computational approaches, we present consistent data on the thermophysical properties of solid and liquid Ni. [ABSTRACT FROM AUTHOR]

Nonadiabatic quantum dynamics are carried out to illustrate the photoionized spectrum of the cyanopropyne (CH3–C≡C–C≡N) as reported in recent experimental measurements [Lamarre et al., J. Mol. Spectrosc. 315, 206 (2015)]. A detailed electronic structure calculation is performed to analyze the topographical details of the first five ionized states, of which three are degenerate states ( X ̃ 2 E , B ̃ 2 E , and C ̃ 2 E) and two are non-degenerate states ( A ̃ 2 A 1 and D ̃ 2 A 1 ). The degenerate E states of the C3V symmetry molecule are prone to Jahn–Teller (JT) instability, and in addition, symmetry allowed A1 − E vibronic coupling, i.e., pseudo-Jahn–Teller (PJT), effects are expected to have a significant impact in the detailed vibronic structure of these electronic states. The JT splittings of X ̃ 2 E and B ̃ 2 E degenerate states are small, whereas it is quite large at three high frequencies in the C ̃ 2 E electronic states. The large energy separation of X ̃ 2 E from the other states and the non-zero PJT coupling of the B ̃ 2 E state with the close-lying A ̃ 2 A 1 state indicate the uncoupled nature of the X ̃ , A ̃ , and B ̃ vibronic bands of C4H3N. The intersection minima of B ̃ and C ̃ states with the D ̃ state nearly coincide with the energetic minimum of D ̃ state. Therefore, the PJT couplings among these states will lead to a strong vibronic interaction to shape the respective band structure. To completely understand the JT and PJT interactions in the photoionized spectrum of C4H3N, the vibronic coupling model Hamiltonian was constructed to perform nuclear dynamics studies for these electronic states. The vibrational progressions in each vibronic band are identified and compared with the available experimental data in the literature. The impacts of JT and PJT effects in the first five ionized states of cyanopropyne are investigated and discussed in detail. [ABSTRACT FROM AUTHOR]

We investigate the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. The bath, characterized by a continuous spectral density function, is composed of spins that are independent level systems described by the s u (2) Lie algebra, representing an environment with a large magnitude of anharmonicity. Based on the previous work by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and by Makri [J. Chem. Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian environment under its linear response limit, we use the time-domain Prony fitting decomposition scheme to the bare–bath time correlation function (TCF) given by the bosonic fluctuation–dissipation theorem to generate the exponential decay basis (or pseudo modes) for DEOM construction. The accuracy and efficiency of this strategy have been explored by a variety of numerical results. We envision that this work provides new insights into extending the hierarchical equations of motion and DEOM approach to certain types of anharmonic environments with arbitrary TCF or spectral density. [ABSTRACT FROM AUTHOR]

Most chemical processes happen at a local scale where only a subset of molecular orbitals is directly involved and only a subset of covalent bonds may be rearranged. To model such reactions, Density Functional Theory (DFT) is often inadequate, and the use of computationally more expensive correlated wavefunction (WF) methods is required for accurate results. Mixed-resolution approaches backed by quantum embedding theory have been used extensively to approach this imbalance. Based on the frozen density embedding freeze-and-thaw algorithm, we describe an approach to embed complete active space self-consistent field simulations run in the OpenMolcas code in a DFT environment calculated in CP2K without requiring any external tools. This makes it possible to study a local, active part of a chemical system in a larger and relatively static environment with a computational cost balanced between the accuracy of a WF method and the efficiency of DFT, which we test on environment–subsystem pairs. Finally, we apply the implementation to an oxygen molecule leaving an aluminum (111) surface and a ruthenium(IV) oxide (110) surface. [ABSTRACT FROM AUTHOR]

An important class of methods for modeling dynamics in open quantum systems is based on the well-known influence functional (IF) approach to solving path-integral equations of motion. Within this paradigm, path-filtering schemes based on the removal of IF elements that fall below a certain threshold aim to reduce the effort needed to calculate and store the influence functional, making very challenging simulations possible. A filtering protocol of this type is considered acceptable as long as the simulation remains mathematically stable. This, however, does not guarantee that the approximated dynamics preserve the physics of the simulated process. In this paper, we explore the possibility of training Generative Flow Networks (GFlowNets) to produce filtering protocols while optimizing for mathematical stability and for physical accuracy. Trained using the trajectory balance objective, the model produces sets of paths to be added to a truncated initial set; it is rewarded if the combined set of paths gives rise to solutions in which the trace of the density matrix is conserved, the populations remain real, and the dynamics approach the exact reference. Using a simple two-level system coupled to a dissipative reservoir, we perform proof-of-concept simulations and demonstrate the elegant and surprising filtering solutions proposed by the GFlowNet. [ABSTRACT FROM AUTHOR]

The multi-layer multi-configurational time-dependent Hartree (MCTDH) approach is an efficient method to study quantum dynamics in real and imaginary time. The present work explores its potential to describe quantum fluids. The multi-layer MCTDH approach in second quantization representation is used to study lattice models beyond one dimension at finite temperatures. A scheme to map the lattice sites onto the MCTDH tree representation for multi-dimensional lattice models is proposed. A statistical sampling scheme previously used in MCTDH calculations is adapted to facilitate an efficient description of the thermal ensemble. As example, a two-dimensional hard-core Bose–Hubbard model is studied considering up to 64 × 64 lattice sites. The single particle function basis set size required to obtain converged results is found to not increase with the lattice size. The numerical results properly simulate the finite temperature Berezinskii–Kosterlitz–Thouless phase transition. [ABSTRACT FROM AUTHOR]

Understanding the dynamics of open quantum systems in strong coupling and non-Markovian regimes remains a formidable theoretical challenge. One popular and well-established method of approximation in these circumstances is provided by the polaron master equation (PME). In this work, we re-evaluate and extend the validity of the PME to capture the impact of non-Markovian polaron dressing, induced by non-equilibrium open system dynamics. By comparing with numerically exact techniques, we confirm that while the standard PME successfully predicts the dynamics of system observables that commute with the polaron transformation (e.g., populations in the Pauli z-basis), it can struggle to fully capture those that do not (e.g., coherences). This limitation stems from the mixing of system and environment degrees of freedom inherent to the polaron transformation, which affects the accuracy of calculated expectation values within the polaron frame. Employing the Nakajima–Zwanzig projection operator formalism, we introduce correction terms that provide an accurate description of observables that do not commute with the transformation. We demonstrate the significance of the correction terms in two cases, the canonical spin-boson model and a dissipative time-dependent Landau–Zener protocol, where they are shown to impact the system dynamics on both short and long timescales. [ABSTRACT FROM AUTHOR]

Although recent advances in simulating open quantum systems have led to significant progress, the applicability of numerically exact methods is still restricted to rather small systems. Hence, more approximate methods remain relevant due to their computational efficiency, enabling simulations of larger systems over extended timescales. In this study, we present advances for one such method, namely, the numerical integration of Schrödinger equation (NISE). First, we introduce a modified ensemble-averaging procedure that improves the long-time behavior of the thermalized variant of the NISE scheme, termed thermalized NISE. Second, we demonstrate how to use the NISE in conjunction with (highly) structured spectral densities by utilizing a noise generating algorithm for arbitrary structured noise. This algorithm also serves as a tool for establishing best practices in determining spectral densities from excited state calculations along molecular dynamics or quantum mechanics/molecular mechanics trajectories. Finally, we assess the ability of the NISE approach to calculate absorption spectra and demonstrate the utility of the proposed modifications by determining population dynamics. [ABSTRACT FROM AUTHOR]

The nitrile (C≡N) stretching vibration is widely used as a site-specific environmental probe of proteins and, as such, many computational studies have been used to investigate the factors that affect its frequency (νCN). These studies, most of which were carried out in the ground electronic state of the molecule of interest, revealed that the formation of a normal or linear hydrogen bond (H-bond) with the nitrile group results in a blueshift in its νCN. Recently, however, several experimental studies showed that for certain aromatic nitriles, solvent relaxations in their excited electronic state(s) induce a redshift (blueshift) in νCN in protic (aprotic) solvents, suggesting that the effect of hydrogen-bonding (H-bonding) interactions on νCN may depend on the electronic state of the molecule. To test this possibility, herein we combine molecular dynamics simulations and quantum mechanical calculations to assess the effect of H-bonding interactions on the νCN of 5-cyanoindole (5-CNI) in its different electronic states. We find that its C≡N group can form either one H-bond (single-H-bond) or two H-bonds (d-H-bonds) with the solvent molecules and that in the ground electronic state, a single-H-bond can lead νCN to shift either to a higher or lower frequency, depending on its angle, which is consistent with previous studies, whereas the d-H-bonds cause νCN to redshift. However, in its lowest-lying excited electronic state (i.e., S1), which has the characteristics of a charge-transfer state, all H-bonds induce a redshift in νCN, with the d-H-bonds being most effective in this regard. [ABSTRACT FROM AUTHOR]

Non-Markovian dynamics arising from the strong coupling of a system to a structured environment is essential in many applications of quantum mechanics and emerging technologies. Deriving an accurate description of general quantum dynamics including memory effects is, however, a demanding task, prohibitive to standard analytical or direct numerical approaches. We present a major release of our open source software package, OQuPy (Open Quantum System in Python), which provides several recently developed numerical methods that address this challenging task. It utilizes the process tensor approach to open quantum systems (OQS) in which a single map, the process tensor, captures all possible effects of an environment on the system. The representation of the process tensor in a tensor network form allows for an exact yet highly efficient description of non-Markovian OQS (NM-OQS). The OQuPy package provides methods to (1) compute the dynamics and multi-time correlations of quantum systems coupled to single and multiple environments, (2) optimize control protocols for NM-OQS, (3) simulate interacting chains of NM-OQS, and (4) compute the mean-field dynamics of an ensemble of NM-OQS coupled to a common central system. Our aim is to provide an easily accessible and extensible tool for researchers of OQS in fields such as quantum chemistry, quantum sensing, and quantum information. [ABSTRACT FROM AUTHOR]

We present a multiscale method coupling the theory of open quantum systems with real-time ab initio treatment of electronic structure to study hot-carrier dynamics in photoexcited plasmonic systems. We combine the Markovian Stochastic Schrödinger equation with an ab initio GW coupled to the Bethe–Salpeter (BSE) equation description of the electronic degrees of freedom, interacting with a metallic nanoparticle modeled classically according to the polarizable continuum model. We apply this methodology to study the effect of relaxation (T1) and pure dephasing (T2) times on the hot-carrier dynamics in a system composed of a quantum portion described at GW/BSE level, i.e., a CHO fragment adsorbed on a vertex of a rhodium nanocube, and of the rest of the nanocube, treated classically, when irradiated with a 2.7 eV light pulse, inspired by the experimental results on plasmon-driven CO2 photoreduction. A net hole injection from rhodium to CHO is observed, with and without the classical portion of the nanocube. The nanocube effect is to enhance the generated charge population by two orders of magnitude. The nonradiative decay, via a relaxation time T1 based on the energy-gap law, produces a rapid decrease of the charge population. Results with T2 only show that a charge injection retarded with respect to the pulse, which is present in the coherent dynamics, disappears when coherence is erased. [ABSTRACT FROM AUTHOR]

We introduce a Python package based on matrix product states (MPS) to simulate both the time-dependent Schrödinger equation (TDSE) and the hierarchical equations of motion (HEOM). The wave function in the TDSE or the reduced density operator/auxiliary density operators in the HEOM are represented using MPS. A matrix product operator (MPO) is then constructed to represent the Hamiltonian in the TDSE or the generalized Liouvillian in the HEOM. The fourth-order Runge–Kutta method and the time-dependent variational principle are used to propagate the MPS. Several examples, including the nonadiabatic interconversion dynamics of the pyrazine molecule, excitation energy transfer dynamics in molecular aggregates and photosynthetic light-harvesting complexes, the spin-boson model, a laser driven two-state model, the Holstein model, and charge transport in the Anderson impurity model, are presented to demonstrate the capability of the package. [ABSTRACT FROM AUTHOR]

The static gas-phase ("simple") ultraviolet absorption spectrum of thiophene is investigated using a combination of a vibronic coupling model Hamiltonian with multi-configuration time-dependent Hartree quantum dynamics simulations. The model includes five states and all 21 vibrations, with potential surfaces calculated at the complete active space with second-order perturbation level of theory. The model includes terms up to eighth-order to describe the diabatic potentials. The resulting spectrum is in excellent agreement with the experimentally measured spectrum of Holland et al. [Phys. Chem. Chem. Phys. 16, 21629 (2014)]. The, until now not understood, spectral features are assigned, with a combination of strongly coupled vibrations and vibronic coupling between the states giving rise to a progression of triplets on the rising edge of the broad spectrum. The analysis of the underlying dynamics indicates that population transfer between all states takes place on a sub-100 fs timescale, with ring-opening occurring at longer times. The model thus provides a starting point for further investigations into the complicated photo-excited dynamics of this key hetero-aromatic molecule. [ABSTRACT FROM AUTHOR]

We compare two recently developed strategies, implemented in open source software packages, for computing linear optical spectra in condensed phase environments in the presence of nonadiabatic effects. Both approaches rely on computing excitation energy and transition dipole fluctuations along molecular dynamics (MD) trajectories, treating molecular and environmental degrees of freedom on the same footing. Spectra are then generated in two ways: in the recently developed Gaussian non-Condon theory, the linear response functions are computed in terms of independent adiabatic excited states, with non-Condon effects described through spectral densities of transition dipole fluctuations. For strongly coupled excited states, we instead parameterize a linear vibronic coupling Hamiltonian directly from spectral densities of energy fluctuations and diabatic couplings computed along the MD trajectory. The optical spectrum is then calculated using powerful, numerically exact tensor-network approaches. Both the electronic structure calculations to sample system fluctuations and the quantum dynamics simulations using tensor-network methods are carried out on graphics processing units, enabling rapid calculations on complex condensed phase systems. We assess the performance of the approaches using model systems in the presence of a conical intersection and the pyrazine molecule in different solvent environments. [ABSTRACT FROM AUTHOR]

The MPSDynamics.jl package provides an easy-to-use interface for performing open quantum systems simulations at zero and finite temperatures. The package has been developed with the aim of studying non-Markovian open system dynamics using the state-of-the-art numerically exact Thermalized-Time Evolving Density operator with Orthonormal Polynomials Algorithm based on environment chain mapping. The simulations rely on a tensor network representation of the quantum states as matrix product states (MPS) and tree tensor network states. Written in the Julia programming language, MPSDynamics.jl is a versatile open-source package providing a choice of several variants of the Time-Dependent Variational Principle method for time evolution (including novel bond-adaptive one-site algorithms). The package also provides strong support for the measurement of single and multi-site observables, as well as the storing and logging of data, which makes it a useful tool for the study of many-body physics. It currently handles long-range interactions, time-dependent Hamiltonians, multiple environments, bosonic and fermionic environments, and joint system–environment observables. [ABSTRACT FROM AUTHOR]

Evaluation of the charge transport property of organic semiconductors requires exact quantum dynamics simulation of large systems. We present a numerically nearly exact approach to investigate carrier transport dynamics in organic semiconductors by extending the non-Markovian stochastic Schrödinger equation with complex frequency modes to a forward–backward scheme and by solving it using the matrix product state (MPS) approach. By utilizing the forward–backward formalism for noise generation, the bath correlation function can be effectively treated as a temperature-independent imaginary part, enabling a more accurate decomposition with fewer complex frequency modes. Using this approach, we study the carrier transport and mobility in the one-dimensional Peierls model, where the nonlocal electron–phonon interaction is taken into account. The reliability of this approach was validated by comparing carrier diffusion motion with those obtained from the hierarchical equations of motion method across various parameter regimes of the phonon bath. The efficiency was demonstrated by the modest virtual bond dimensions of MPS and the low scaling of the computational time with the system size. [ABSTRACT FROM AUTHOR]

Numerous variational methods have been proposed for solving quantum many-body systems, but they often face exponentially increasing computational complexity as the Hilbert space dimension grows. To address this, we introduce a novel approach using quantum neural networks to simulate the dissipative dynamics of many-body open quantum systems. This method combines neural-network quantum state representation with the time-dependent variational principle, both implemented via quantum algorithms. This results in accurate open quantum dynamics described by the Lindblad quantum master equation, exemplified by the spin-boson and transverse field Ising models. Our approach avoids the computational expense of classical algorithms and demonstrates the potential advantages of quantum computing for many-body simulations. To reduce measurement errors, we introduce a projection reset procedure, which could benefit other quantum simulations. In addition, our approach can be extended to simulate non-Markovian quantum dynamics. [ABSTRACT FROM AUTHOR]

Accurately simulating non-Markovian quantum dynamics in system–bath coupled problems remains challenging. In this work, we present a novel memory truncation scheme for the iterative quasi-adiabatic propagator path integral (iQuAPI) method to improve accuracy. Conventional memory truncation in iQuAPI discards all influence functional beyond a certain time interval, which is not effective for problems with a long memory time. Our proposed scheme selectively retains the most significant parts of the influence functional using the density matrix renormalization group algorithm. We validate the effectiveness of our scheme through simulations of the spin-boson model across various parameter sets, demonstrating faster convergence and improved accuracy compared to the conventional scheme. Our findings suggest that the new memory truncation scheme significantly advances the capabilities of iQuAPI for problems with a long memory time. [ABSTRACT FROM AUTHOR]

The ultrafast quantum dynamics of photophysical processes in complex molecules is an extremely challenging computational problem with a broad variety of fascinating applications in quantum chemistry and biology. Inspired by recent developments in open quantum systems, we introduce a pure-state unraveled hybrid-bath method that describes a continuous environment via a set of discrete, effective bosonic degrees of freedom using a Markovian embedding. Our method is capable of describing both, a continuous spectral density and sharp peaks embedded into it. Thereby, we overcome the limitations of previous methods, which either capture long-time memory effects using the unitary dynamics of a set of discrete vibrational modes or use memoryless Markovian environments employing a Lindblad or Redfield master equation. We benchmark our method against two paradigmatic problems from quantum chemistry and biology. We demonstrate that compared to unitary descriptions, a significantly smaller number of bosonic modes suffices to describe the excitonic dynamics accurately, yielding a computational speed-up of nearly an order of magnitude. Furthermore, we take into account explicitly the effect of a δ-peak in the spectral density of a light-harvesting complex, demonstrating the strong impact of the long-time memory of the environment on the dynamics. [ABSTRACT FROM AUTHOR]

Unidirectional photochemical molecular motors can act as a power source for molecular machines. The motors operate by successive excited state isomerization and ground state helix inversion reactions, attaining unidirectionality from an interplay of steric strain and stereochemistry. Optimizing the yield of the excited state isomerization reaction is an important goal that requires detailed knowledge of excited state dynamics. Here, we investigate the effect of electron withdrawing and donating substituents on excited state structure and ultrafast dynamics in a series of newly synthesized first generation photochemical molecular motors. All substituents red-shift the absorption spectra, while some modify the Stokes shift and render the fluorescence quantum yield solvent polarity dependent. Raman spectra and density functional theory calculations reveal that the stretching mode of the C=C "axle" in the electronic ground state shows a small red-shift when conjugated with electron withdrawing substituents. Ultrafast fluorescence measurements reveal substituent and solvent polarity effects, with the excited state decay being accelerated by both polar solvent environment and electron withdrawing substituents. Excited state structural dynamics are investigated by fluorescence coherence spectroscopy and femtosecond stimulated Raman spectroscopy. The time resolved Raman measurements are shown to provide structural data specifically on the Franck–Condon excited state. The C=C localized modes have a different substituent dependence compared to the ground state, with the unsubstituted motor having the most red-shifted mode. Such measurements provide valuable new insights into pathways to optimize photochemical molecular motor performance, especially if they can be coupled with high-quality quantum molecular dynamics calculations. [ABSTRACT FROM AUTHOR]

In this paper, we report a new algorithm for creating an adaptive basis set in the Multiconfigurational Ehrenfest (MCE) method, which is termed Full Cloning (FC), and test it together with the existing Multiple Cloning (MC) using the spin-boson model at zero-temperature as a benchmark. The zero-temperature spin-boson regime is a common hurdle in the development of methods that seek to model quantum dynamics. Two versions of MCE exist. We demonstrate that MC is vital for the convergence of MCE version 2 (MCEv2). The first version (MCEv1) converges much better than MCEv2, but FC improves its convergence in a few cases where it is hard to converge it with the help of a reasonably small size of the basis set. [ABSTRACT FROM AUTHOR]

The motional narrowing effect has been extensively studied for cavity exciton–polariton systems in recent decades both experimentally and theoretically, which is featured by (1) the subaverage behavior and (2) the asymmetric linewidths for the upper polariton and the lower polariton. However, a minimal theoretical model that is clear and adequate to address all these effects as well as the linewidth scaling relations remains missing. In this work, based on the single mode 1D Holstein–Tavis–Cummings (HTC) model, we studied the motional narrowing effect of the polariton linear absorption spectra via both semi-analytic derivations and numerically exact quantum dynamics simulations using the hierarchical equations of motion approach. The results reveal that under collective light–matter coupling between a cavity mode and N molecules, the polariton linewidth scales as 1 / N under the slow limit, while scales as 1/N under the fast limit, due to the polaron decoupling effect. Furthermore, by varying the detunings, the polariton linewidths exhibit significant motional narrowing, covering both characters mentioned above. Our analytic linewidth expressions [Eqs. (34) and (35)] agree well with the numerical exact simulations in all the parameter regimes we explored. These results indicate that the physics of motional narrowing is adequately accounted for by the single-mode 1D HTC model. We envision that both the numerical results and the analytic polariton linewidths expression presented in this work will offer great theoretical value for providing a better understanding of the exciton–polariton motional narrowing based on the HTC model. [ABSTRACT FROM AUTHOR]

Non-adiabatic (NA) molecular dynamics (MD) is a powerful approach for studying far-from-equilibrium quantum dynamics in photophysical and photochemical systems. Most NA-MD methods are developed and tested with few-state models, and their validity with complex systems involving many states is not well studied. By modeling intraband equilibration and interband recombination of charge carriers in MoS2, we investigate the convergence of three popular NA-MD algorithms, fewest switches surface hopping (FSSH), global flux surface hopping (GFSH), and decoherence induced surface hopping (DISH) with the number of states. Only the standard DISH algorithm converges with the number of states and produces Boltzmann equilibrium. Unitary propagation of the wave function in FSSH and GFSH violates the Boltzmann distribution, leads to internal inconsistency between time-dependent Schrödinger equation state populations and trajectory counts, and produces non-convergent results. Introducing decoherence in FSSH and GFSH by collapsing the wave function fixes these problems. The simplified version of DISH that omits projecting out the occupied state and is applicable to few-state systems also causes problems when the number of states is increased. We discuss the algorithmic application of wave function collapse and Boltzmann detailed balance and provide detailed FSSH, GFSH, and DISH flow charts. The use of convergent NA-MD methods is highly important for modeling complicated quantum processes involving multiple states. Our findings provide the basis for investigating quantum dynamics in realistic complex systems. [ABSTRACT FROM AUTHOR]

Quantum dynamics simulation and computational spectroscopy serve as indispensable tools for the theoretical understanding of various fundamental physical and chemical processes, ranging from charge transfer to photochemical reactions. When simulating realistic systems, the primary challenge stems from the overwhelming number of degrees of freedom and the pronounced many-body correlations. Here, we present Kylin-V, an innovative quantum dynamics package designed for accurate and efficient simulations of dynamics and spectroscopic properties of vibronic Hamiltonians for molecular systems and their aggregates. Kylin-V supports various quantum dynamics and computational spectroscopy methods, such as time-dependent density matrix renormalization group and our recently proposed single-site and hierarchical mapping approaches, as well as vibrational heat-bath configuration interaction. In this paper, we introduce the methodologies implemented in Kylin-V and illustrate their performances through a diverse collection of numerical examples. [ABSTRACT FROM AUTHOR]

In this work, we present a mixed quantum–classical open quantum system dynamics method for studying rate modifications of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. In this approach, the cavity radiation mode is treated classically with a mean-field nuclear force averaging over the remaining degrees of freedom, both within the system and the environment, which are handled quantum mechanically within the hierarchical equations of motion framework. Using this approach, we conduct a comparative analysis by juxtaposing the mixed quantum–classical results with fully quantum-mechanical simulations. After eliminating spurious peaks that can occur when not using the rigorous definition of the rate constant, we confirm the crucial role of the quantum nature of the cavity radiation mode in reproducing the resonant peak observed in the cavity frequency-dependent rate profile. In other words, it appears necessary to explicitly consider the quantized photonic states in studying reactivity modification in vibrational polariton chemistry (at least for the model systems studied in this work), as these phenomena stem from cavity-induced reaction pathways involving resonant energy exchanges between photons and molecular vibrational transitions. [ABSTRACT FROM AUTHOR]

Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum–classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables. [ABSTRACT FROM AUTHOR]

Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's golden rule (GR), which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory; however, in short range electron/energy transfer reactions, this coupling can become very large, and, therefore, Fermi's GR fails to make even qualitatively accurate rate predictions. In this paper, I present a simple modified GR theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. This theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating GR rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore, the optimal GR (OGR) theory can also be combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus–Levich–Jortner theory, offering clear physical insights into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a boron-dipyrromethane–anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of 4. Overall, OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insights into a range of non-adiabatic processes. [ABSTRACT FROM AUTHOR]

Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system–bath configurations without resorting to a perturbative description of the system–bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system–bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit. [ABSTRACT FROM AUTHOR]

Dilution refrigerators are widely used in the fields of condensed matter physics and quantum technology. The condensation-driven dilution refrigerator uses a condenser operating at temperatures below the Still to liquefy the 3He vapor and achieve the circulation of 3He, which has the advantages of compact structure, lightweight, low cost, and low vibration. The published research primarily focuses on the system architecture and performance, and the research and analysis on the thermodynamic cycle are still incomplete. In this paper, the condensation-driven dilution refrigeration cycle has been clarified as a thermally driven refrigeration cycle, and the thermodynamic performances including the figure of merit and thermodynamic perfectibility are investigated. Optimizations have been made to the key components of the previous prototype, and the lowest no-load temperature of 68 mK and a cooling power of 4 μW at 100 mK were achieved. Compared with the previous prototype, the thermodynamic perfectibility of the system increased from 7.63% to 17.83%. The impact of the Still heating strategies on the system was analyzed, and a start-up strategy was proposed to speed up the cooldown process. [ABSTRACT FROM AUTHOR]

The correlation discrete variable representation (CDVR) enables multi-layer multi-configurational time-dependent Hartree (MCTDH) quantum dynamics simulations on general potential energy surfaces. In a recent study [R. Ellerbrock and U. Manthe, J. Chem. Phys. 156, 134107 (2022)], an improved CDVR that can account for the symmetry properties of a tree-shaped wavefunction representation has been introduced. This non-hierarchical CDVR drastically reduces the number of grid points required in the time-dependent quadrature used to evaluate all potential energy matrix elements. While the first studies on the non-hierarchical CDVR approach have been restricted to single-layer calculations, here the complete theory required for the implementation of the non-hierarchical CDVR approach in the multi-layer MCTDH context will be presented. Detailed equations facilitating the efficient recursive computation of all matrix elements are derived, and a new notation adapted to the symmetry properties of the tree-shaped representation is introduced. Calculations studying the non-adiabatic quantum dynamics of photoexcited pyrazine in 24 dimensions illustrate the properties of the non-hierarchical multi-layer CDVR. [ABSTRACT FROM AUTHOR]

The use of semiconductor nanocrystals in scalable quantum technologies requires characterization of the exciton coherence dynamics in an ensemble of electronically isolated crystals in which system–bath interactions are nevertheless strong. In this communication, we identify signatures of Fano-like interference between excitons and photocarriers in the coherent two-dimensional photoluminescence excitation spectral lineshapes of mixed lead-halide perovskite nanocrystals in dilute solution. Specifically, by tuning the femtosecond-pulse spectrum, we show such interference in an intermediate coupling regime, which is evident in the coherent lineshape when simultaneously exciting the exciton and the free-carrier band at higher energy. We conclude that this interference is an intrinsic effect that will be consequential in the quantum dynamics of the system and will thus dictate decoherence dynamics, with consequences in their application in quantum technologies. [ABSTRACT FROM AUTHOR]

In the previous paper [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111-1–214111-13 (2024)], we developed a theory called MQME-D, which allows us to decompose the overall energy dissipation process in open quantum system dynamics into contributions by individual components of the bath when the subsystem dynamics is governed by a Markovian quantum master equation (MQME). Here, we contrast the predictions of MQME-D against the numerically exact results obtained by combining hierarchical equations of motion (HEOM) with a recently reported protocol for monitoring the statistics of the bath. Overall, MQME-D accurately captures the contributions of specific bath components to the overall dissipation while greatly reducing the computational cost compared to exact computations using HEOM. The computations show that MQME-D exhibits errors originating from its inherent Markov approximation. We demonstrate that its accuracy can be significantly increased by incorporating non-Markovianity by exploiting time scale separations (TSS) in different components of the bath. Our work demonstrates that MQME-D combined with TSS can be reliably used to understand how energy is dissipated in realistic open quantum system dynamics. [ABSTRACT FROM AUTHOR]

A major difficulty in quantum simulation is the adequate treatment of a large collection of entangled particles, synonymous with electron correlation in electronic structure theory, with coupled cluster (CC) theory being the leading framework for dealing with this problem. Augmenting computationally affordable low-rank approximations in CC theory with a perturbative account of higher-rank excitations is a tractable and effective way of accounting for the missing electron correlation in those approximations. This is perhaps best exemplified by the "gold standard" CCSD(T) method, which bolsters the baseline CCSD with the effects of triple excitations using considerations from many-body perturbation theory (MBPT). Despite this established success, such a synergy between MBPT and the unitary analog of CC theory (UCC) has not been explored. In this work, we propose a similar approach wherein converged UCCSD amplitudes are leveraged to evaluate energy corrections associated with triple excitations, leading to the UCCSD[T] method. In terms of quantum computing, this correction represents an entirely classical post-processing step that improves the energy estimate by accounting for triple excitation effects without necessitating new quantum algorithm developments or increasing demand for quantum resources. The rationale behind this choice is shown to be rigorous by studying the properties of finite-order UCC energy functionals, and our efforts do not support the addition of the fifth-order contributions as in the (T) correction. We assess the performance of these approaches on a collection of small molecules and demonstrate the benefits of harnessing the inherent synergy between MBPT and UCC theories. [ABSTRACT FROM AUTHOR]

We present a general and practical theoretical framework to investigate how energy is dissipated in open quantum system dynamics. This is performed by quantifying the contributions of individual bath components to the overall dissipation of the system. The framework is based on the Nakajima–Zwanzig projection operator technique, which allows us to express the rate of energy dissipation into a specific bath degree of freedom by using traces of operator products. The approach captures system-bath interactions to all orders, but is based on second-order perturbation theory on the off-diagonal subsystem's couplings and a Markovian description of the bath. The usefulness of our theory is demonstrated by applying it to various models of open quantum systems involving harmonic oscillators or spin baths and connecting the outcomes to existing results such as our previously reported formula derived for locally coupled harmonic baths [Kim and Franco, J. Chem. Phys. 154, 084109 (2021)]. We also prove that the dissipation calculated by our theory rigorously satisfies thermodynamic principles such as energy conservation and detailed balance. Overall, the strategy can be used to develop the theory and simulation of dissipation pathways to interpret and engineer the dynamics of open quantum systems. [ABSTRACT FROM AUTHOR]

Static and time-dependent quantum-mechanical approaches have been employed in the literature to characterize the physics of light-emitting molecules and nanostructures. However, the electromagnetic emission induced by an input current has remained beyond the realm of molecular simulations. This is the challenge addressed here with the help of an equation of motion for the density matrix coupled to a photon bath based on a Redfield formulation. This equation is evolved within the framework of the driven-Liouville von Neumann approach, which incorporates open boundaries by introducing an applied bias and a circulating current. The dissipated electromagnetic power can be computed in this context from the time derivative of the energy. This scheme is applied in combination with a self-consistent tight-binding Hamiltonian to investigate the effects of bias and molecular size on the electroluminescence of metallic and semiconducting chains. For the latter, a complex interplay between bias and molecular length is observed: there is an optimal number of atoms that maximizes the emitted power at high voltages but not at low ones. This unanticipated behavior can be understood in terms of the band bending produced along the semiconducting chain, a phenomenon that is captured by the self-consistency of the method. A simple analytical model is proposed that explains the main features revealed by the simulations. The methodology, applied here at a self-consistent tight-binding level but extendable to more sophisticated Hamiltonians such as density functional tight binding and time dependent density functional theory, promises to be helpful for quantifying the power and quantum efficiency of nanoscale electroluminescent devices. [ABSTRACT FROM AUTHOR]

Recent efforts have sought to develop paramagnetic molecular quantum bits (qubits) as a means to store and manipulate quantum information. Emerging structure-property relationships have shed light on electron spin decoherence mechanisms. While insights within molecular quantum information science have derived from synthetic systems, biomolecular platforms would allow for the study of decoherence phenomena in more complex chemical environments and further leverage molecular biology and protein engineering approaches. Here we have employed the exchange-coupled ST = 1/2 Fe2S2 active site of putidaredoxin, an electron transfer metalloprotein, as a platform for fundamental mechanistic studies of electron spin decoherence toward spin-based biological quantum sensing. At low temperatures, decoherence rates were anisotropic, reflecting a hyperfine-dominated decoherence mechanism, standing in contrast to the anisotropy of molecular systems observed previously. This mechanism provided a pathway for probing spatial effects on decoherence, such as protein vs solvent contributions. Furthermore, we demonstrated spatial sensitivity to single point mutations via site-directed mutagenesis and temporal sensitivity for monitoring solvent isotope exchange. Thus, this study demonstrates a step toward the design and construction of biomolecular quantum sensors.

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

We develop a quasiparticle approach to capture the dynamics of open quantum systems coupled to bosonic thermal baths of arbitrary complexity based on the Hierarchical Equations of Motion (HEOM). This is done by generalizing the HEOM dynamics and mapping it into that of the system in interaction with a few bosonic fictitious quasiparticles that we call bexcitons. Bexcitons arise from a decomposition of the bath correlation function into discrete features. Specifically, bexciton creation and annihilation couple the auxiliary density matrices in the HEOM. The approach provides a systematic strategy to construct exact quantum master equations that include the system–bath coupling to all orders even for non-Markovian environments. Specifically, by introducing different metrics and representations for the bexcitons it is possible to straightforwardly generate different variants of the HEOM, demonstrating that all these variants share a common underlying quasiparticle picture. Bexcitonic properties, while unphysical, offer a coarse-grained view of the correlated system–bath dynamics and its numerical convergence. For instance, we use it to analyze the instability of the HEOM when the bath is composed of underdamped oscillators and show that it leads to the creation of highly excited bexcitons. The bexcitonic picture can also be used to develop more efficient approaches to propagate the HEOM. As an example, we use the particle-like nature of the bexcitons to introduce mode-combination of bexcitons in both number and coordinate representation that uses the multi-configuration time-dependent Hartree to efficiently propagate the HEOM dynamics. [ABSTRACT FROM AUTHOR]

The time-convolutionless master equation provides a general framework to model the non-Markovian dynamics of an open quantum system with a time-local generator. A diagrammatic representation is developed and proven for the perturbative expansion of the exact time-local generator for an open quantum system interacting with arbitrary environments. A truncation of the perturbation expansion leads to perturbative time-convolutionless quantum master equations. We further introduce a general iterative approach to construct nonperturbative approximations for the time-local generator as nested time-ordered exponential operators. [ABSTRACT FROM AUTHOR]

This study presents a parallel algorithm for high-dimensional quantum dynamics simulations in poly atomic reactions, integrating distributed- and shared-memory models. The distributions of the wave function and potential energy matrix across message passing interface processes are based on bundled radial and angular dimensions, with implementations featuring either two- or one-sided communication schemes. Using realistic parameters for the H + NH3 reaction, performance assessment reveals linear scalability, exceeding 90% efficiency with up to 600 processors. In addition, owing to the universal and concise structure, the algorithm demonstrates remarkable extensibility to diverse reaction systems, as demonstrated by successes with six-atom and four-atom reactions. This work establishes a robust foundation for high-dimensional dynamics studies, showcasing the algorithm's efficiency, scalability, and adaptability. The algorithm's potential as a valuable tool for unraveling quantum dynamics complexities is underscored, paving the way for future advancements in the field. [ABSTRACT FROM AUTHOR]