Generalized system-bath entanglement theorem for Gaussian environments.

The entanglement between system and bath often plays a pivotal role in complex systems spanning multiple orders of magnitude. A system-bath entanglement theorem was previously established for Gaussian environments in J. Chem. Phys. 152, 034102 (2020) regarding linear response functions. This theorem connects the entangled responses to the local system and bare bath properties. In this work, we generalize it to correlation functions. Key steps in derivations involve using the generalized Langevin dynamics for hybridizing bath modes and the Bogoliubov transformation that maps the original finite-temperature reservoir to an effective zero-temperature vacuum by employing an auxiliary bath. The generalized theorem allows us to evaluate the system-bath entangled correlations and the bath mode correlations in the total composite space, as long as we know the bare-bath statistical properties and obtain the reduced system correlations. To demonstrate the cross-scale entanglements, we utilize the generalized theorem to calculate the solvation free energy of an electron transfer system with intramolecular vibrational modes.

Quantum neural network approach to Markovian dissipative dynamics of many-body open quantum systems.

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.

Multimode Brownian oscillators: Exact solutions to heat transport.

In this work, we investigate the multimode Brownian oscillators in nonequilibrium scenarios with multiple reservoirs at different temperatures. For this purpose, an algebraic method is proposed. This approach gives the exact time-local equation of motion for the reduced density operator, from which we can easily extract not only the reduced system but also hybrid bath dynamical information. The resulting steady-state heat current is found to be numerically consistent with another discrete imaginary-frequency method followed by Meir-Wingreen's formula. It is anticipated that the development in this work would constitute an indispensable component of nonequilibrium statistical mechanics for open quantum systems.

A semilocal machine-learning correction to density functional approximations.

Machine learning (ML) has demonstrated its potential usefulness for the development of density functional theory methods. In this work, we construct an ML model to correct the density functional approximations, which adopts semilocal descriptors of electron density and density derivative and is trained by accurate reference data of relative and absolute energies. The resulting ML-corrected functional is tested on a comprehensive dataset including various types of energetic properties. Particularly, the ML-corrected Becke's three parameters and the Lee-Yang-Parr correlation (B3LYP) functional achieves a substantial improvement over the original B3LYP on the prediction of total energies of atoms and molecules and atomization energies, and a marginal improvement on the prediction of ionization potentials, electron affinities, and bond dissociation energies; whereas, it preserves the same level of accuracy for isomerization energies and reaction barrier heights. The ML-corrected functional allows for fully self-consistent-field calculation with similar efficiency to the parent functional. This study highlights the progress of building an ML correction toward achieving a functional that performs uniformly better than B3LYP.

Open quantum systems with nonlinear environmental backactions: Extended dissipaton theory vs core-system hierarchy construction.

In this paper, we present a comprehensive account of quantum dissipation theories with the quadratic environment couplings. The theoretical development includes the Brownian solvation mode embedded hierarchical quantum master equations, a core-system hierarchy construction that verifies the extended dissipaton equation of motion (DEOM) formalism [R. X. Xu et al., J. Chem. Phys. 148, 114103 (2018)]. Developed are also the quadratic imaginary-time DEOM for equilibrium and the λ(t)-DEOM for nonequilibrium thermodynamics problems. Both the celebrated Jarzynski equality and Crooks relation are accurately reproduced, which, in turn, confirms the rigorousness of the extended DEOM theories. While the extended DEOM is more numerically efficient, the core-system hierarchy quantum master equation is favorable for "visualizing" the correlated solvation dynamics.

Extended dissipaton equation of motion for electronic open quantum systems: Application to the Kondo impurity model.

In this paper, we present an extended dissipaton equation of motion for studying the dynamics of electronic impurity systems. Compared with the original theoretical formalism, the quadratic couplings are introduced into the Hamiltonian accounting for the interaction between the impurity and its surrounding environment. By exploiting the quadratic fermionic dissipaton algebra, the proposed extended dissipaton equation of motion offers a powerful tool for studying the dynamical behaviors of electronic impurity systems, particularly in situations where nonequilibrium and strongly correlated effects play significant roles. Numerical demonstrations are carried out to investigate the temperature dependence of the Kondo resonance in the Kondo impurity model.

Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation.

Dissipaton theory had been proposed as an exact, nonperturbative approach to deal with open quantum system dynamics, where the influence of the Gaussian environment is characterized by statistical quasi-particles, named dissipatons. In this work, we revisit the dissipaton equation of motion theory and establish an equivalent dissipaton-embedded quantum master equation (DQME) that gives rise to dissipatons as generalized Brownian particles. As explained in this work, the DQME supplies a direct approach to investigate the statistical characteristics of dissipatons and, thus, the physically supporting hybrid bath modes. Numerical demonstrations are carried out on the electron transfer model, exhibiting the transient statistical properties of the solvation coordinate.

Hierarchical equations of motion approach for accurate characterization of spin excitations in quantum impurity systems.

Recent technological advancement in scanning tunneling microscopes has enabled the measurement of spin-field and spin-spin interactions in single atomic or molecular junctions with an unprecedentedly high resolution. Theoretically, although the fermionic hierarchical equations of motion (HEOM) method has been widely applied to investigate the strongly correlated Kondo states in these junctions, the existence of low-energy spin excitations presents new challenges to numerical simulations. These include the quest for a more accurate and efficient decomposition for the non-Markovian memory of low-temperature environments and a more careful handling of errors caused by the truncation of the hierarchy. In this work, we propose several new algorithms, which significantly enhance the performance of the HEOM method, as exemplified by the calculations on systems involving various types of low-energy spin excitations. Being able to characterize both the Kondo effect and spin excitation accurately, the HEOM method offers a sophisticated and versatile theoretical tool, which is valuable for the understanding and even prediction of the fascinating quantum phenomena explored in cutting-edge experiments.

Improving Density Functional Prediction of Molecular Thermochemical Properties with a Machine-Learning-Corrected Generalized Gradient Approximation.

The past decade has seen an increasing interest in designing sophisticated density functional approximations (DFAs) by integrating the power of machine learning (ML) techniques. However, application of the ML-based DFAs is often confined to simple model systems. In this work, we construct an ML correction to the widely used Perdew-Burke-Ernzerhof (PBE) functional by establishing a semilocal mapping from the electron density and reduced gradient to the exchange-correlation energy density. The resulting ML-corrected PBE is immediately applicable to any real molecule and yields significantly improved heats of formation while preserving the accuracy for other thermochemical and kinetic properties. This work highlights the prospect of combining the power of data-driven ML methods with physics-inspired derivations for reaching the heaven of chemical accuracy.

Electron Transfer under the Floquet Modulation in Donor-Bridge-Acceptor Systems.

Electron transfer (ET) processes are of broad interest in modern chemistry. With the advancements of experimental techniques, one may modulate the ET via such events as light-matter interactions. In this work, we study the ET under a Floquet modulation occurring in the donor-bridge-acceptor systems, with the rate kernels projected out from the exact dissipaton equation of motion formalism. This together with the Floquet theorem enables us to investigate the interplay between the intrinsic non-Markovianity and the driving periodicity. The observed rate kernel exhibits a Herzberg-Teller-like mechanism induced by the bridge fluctuation subject to effective modulation.

Universal time-domain Prony fitting decomposition for optimized hierarchical quantum master equations.

In this Communication, we propose the time-domain Prony fitting decomposition (t-PFD) as an accurate and efficient exponential series method, applicable to arbitrary bath correlation functions. The resulting numerical efficiency of hierarchical equations of motion (HEOM) formalism is greatly optimized, especially in low temperature regimes that would be inaccessible with other methods. For demonstration, we calibrate the present t-PFD against the celebrated Padé spectrum decomposition method, followed by converged HEOM evaluations on the single-impurity Anderson model system.

A statistical quasi-particles thermofield theory with Gaussian environments: System-bath entanglement theorem for nonequilibrium correlation functions.

For open quantum systems, the Gaussian environmental dissipative effect can be represented by statistical quasi-particles, namely, dissipatons. We exploit this fact to establish the dissipaton thermofield theory. The resulting generalized Langevin dynamics of absorptive and emissive thermofield operators are effectively noise-resolved. The system-bath entanglement theorem is then readily followed between an important class of nonequilibrium steady-state correlation functions. All these relations are validated numerically. A simple corollary is the transport current expression, which exactly recovers the result obtained from the nonequilibrium Green's function formalism.

Nonequilibrium work distributions in quantum impurity system-bath mixing processes.

The fluctuation theorem, where the central quantity is the work distribution, is an important characterization of nonequilibrium thermodynamics. In this work, based on the dissipaton-equation-of-motion theory, we develop an exact method to evaluate the work distributions in quantum impurity system-bath mixing processes in the presence of non-Markovian and strong couplings. Our results not only precisely reproduce the Jarzynski equality and Crooks relation but also reveal rich information on large deviation. The numerical demonstrations are carried out with a spin-boson model system.

Coherent excitation energy transfer in model photosynthetic reaction center: Effects of non-Markovian quantum environment.

Excitation energy transfer (EET) and electron transfer (ET) are crucially involved in photosynthetic processes. In reality, the photosynthetic reaction center constitutes an open quantum system of EET and ET, which manifests interplay of pigments, solar light, and phonon baths. So far, theoretical studies have been mainly based on master equation approaches in the Markovian condition. The non-Markovian environmental effect, which may play a crucial role, has not been sufficiently considered. In this work, we propose a mixed dynamic approach to investigate this open system. The influence of phonon bath is treated via the exact dissipaton equation of motion (DEOM), while that of photon bath is via the Lindblad master equation. Specifically, we explore the effect of non-Markovian quantum phonon bath on the coherent transfer dynamics and its manipulation on the current-voltage behavior. Distinguished from the results of the completely Markovian-Lindblad equation and those adopting the classical environment description, the mixed DEOM-Lindblad simulations exhibit transfer coherence up to a few hundred femtoseconds and the related environmental manipulation effect on the current. These non-Markovian quantum coherent effects may be extended to more complex and realistic systems and be helpful in the design of organic photovoltaic devices.

Unveiling the High Catalytic Activity of a Dinuclear Iron Complex for the Oxygen Evolution Reaction.

The dinuclear iron complex [(H2O)-FeIII-(ppq)-O-(ppq)-FeIII-Cl]3+ (FeIII(ppq), ppq = 2-(pyrid-2'-yl)-8-(1″,10″-phenanthrolin-2″-yl)-quinoline) demonstrates a catalytic activity about one order of magnitude higher than the mononuclear iron complex [Cl-FeIII(dpa)-Cl]+ (FeIII(dpa), dpa = N,N-di(1,10-phenanthrolin-2-yl)-N-isopentylamine) for the oxygen evolution reaction (OER). However, the mechanism behind such an unusually high activity has remained largely unclear. To solve this puzzle, a decomposition-and-reaction mechanism is proposed for the OER with the dinuclear FeIII(ppq) complex as the initial state of the catalytic agent. In this mechanism, the high-valent dinuclear iron complex first dissociates into two mononuclear moieties, and the oxidized mononuclear iron complexes directly catalyze the formation of an O-O bond through a nitrate attack pathway with nitrate functioning as a cocatalyst. Density functional theory calculations reveal that it is the electron-deficient microenvironment around the iron center that gives rise to the remarkable catalytic activity observed experimentally. Therefore, the outstanding performance of the FeIII(ppq) catalyst can be ascribed to the high reactivity of its mononuclear moieties in a high oxidation state, which is concomitant with the structural stability of the low-valent dinuclear complex. The theoretical insights provided by this study could be useful for the optimization and design of novel iron-based water oxidation catalysts.

Quantum dissipation with nonlinear environment couplings: Stochastic fields dressed dissipaton equation of motion approach.

Accurate and efficient simulation on quantum dissipation with nonlinear environment couplings remains a challenging task nowadays. In this work, we propose to incorporate the stochastic fields, which resolve just the nonlinear environment coupling terms, into the dissipaton-equation-of-motion (DEOM) construction. The stochastic fields are introduced via the Hubbard-Stratonovich transformation. After the transformation, the resulted stochastic-fields-dressed (SFD) total Hamiltonian contains only linear environment coupling terms. On the basis of that, SFD-DEOM can then be constructed. The resultant SFD-DEOM, together with the ensemble average over the stochastic fields, constitutes an exact and nonperturbative approach to quantum dissipation under nonlinear environment couplings. It is also of relatively high efficiency and stability due to the fact that only nonlinear environment coupling terms are dealt with stochastic fields, while linear couplings are still treated as the usual DEOM. Numerical performance and demonstrations are presented with a two-state model system.

Correlated vibration-solvent effects on the non-Condon exciton spectroscopy.

Excitation energy transfer is crucially involved in a variety of systems. During the process, the non-Condon vibronic coupling and the surrounding solvent interaction may synergetically play important roles. In this work, we study the correlated vibration-solvent influences on the non-Condon exciton spectroscopy. Statistical analysis is elaborated for the overall vibration-plus-solvent environmental effects. Analytic solutions are derived for the linear absorption of monomer systems. General simulations are accurately carried out via the dissipaton-equation-of-motion approach. The resulted spectra in either the linear absorption or strong field regime clearly demonstrate the coherence enhancement due to the synergetic vibration-solvent correlation.

Fractionated carbon dioxide (CO2) laser treatment contributes to trans-nail penetration of rhodamine B and changes of cytokine microenvironment.

This study is to determine the role of the fractional CO2 laser in topical drug delivery and the impact of local immune responses. Experimental rabbit nails were treated with fractionated CO2 laser at varied fluencies of 20 mJ, 25 mJ, and 30 mJ and half of which were coated with rhodamine B (RhB). Histological examination was performed by hematoxylin and eosin staining; the penetration of RhB was assessed by the use of confocal laser scanning microscopy; and the expressions of IFN-γ and IL-4 mRNA in situ were detected by means of qPCR at 12 h, 24 h, 3 days, and 7 days post-laser irritation. The fractional CO2 laser could generate microscopic treatment zones in nail plates, and the depths of these micropores as well as the permeation of RhB in nails increased significantly in an energy-dependent manner. Importantly, the laser irritation led an upregulation of local IFN-γ mRNA expression accompanied by a downregulation of IL-4 mRNA expression. The ultrapulsed ablative fractionated CO2 laser may assist topical drug delivery, and may drive stronger local Th1 responses due to an imbalance of IFN-γ/IL-4 expressions, suggesting that the combination of ablative fractionated CO2 laser with topical agents would be an effective option for the treatment of onychomycosis.

Entangled system-and-environment dynamics: Phase-space dissipaton theory.

Dissipaton-equation-of-motion (DEOM) theory [Y. J. Yan, J. Chem. Phys. 140, 054105 (2014)] is an exact and nonperturbative many-particle method for open quantum systems. The existing dissipaton algebra also treats the dynamics of hybrid bath solvation coordinates. The dynamics of conjugate momentums remain to be addressed within the DEOM framework. In this work, we establish this missing ingredient, the dissipaton algebra on solvation momentums, with rigorous validations against necessary and sufficient criteria. The resulted phase-space DEOM theory will serve as a solid ground for further developments of various practical methods toward a broad range of applications. We illustrate this novel dissipaton algebra with the phase-space DEOM-evaluation on heat current fluctuation.

Thermodynamic free-energy spectrum theory for open quantum systems.

In this work, we develop the free-energy spectrum theory for thermodynamics of open quantum impurity systems that can be either fermionic or bosonic or combined. We identify two types of thermodynamic free-energy spectral functions for open quantum systems and further consider the thermodynamic limit, which supports the Gaussian-Wick description of hybrid environments. We can then relate the thermodynamic spectral functions to the local impurity properties. These could be experimentally measurable quantities, especially for the cases of quantum dots embedded in solid surfaces. Another type of input is the bare-bath coupling spectral densities, which could be accurately determined with various methods. For illustration, we consider the simplest noninteracting systems, with focus on the strikingly different characteristics between the bosonic and fermionic scenarios.