Nonadiabatic Systems Research Articles

Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium.

A vibrational electronic-thermofield coupled cluster (VE-TFCC) approach is developed to calculate thermal properties of non-adiabatic vibronic coupling systems. The thermofield (TF) theory and a mixed linear exponential ansatz based on second-quantized Bosonic construction operators are introduced to propagate the thermal density operator as a "pure state" in the Bogoliubov representation. Through this compact representation of the thermal density operator, the approach is basis-set-free and scales classically (polynomial) as the number of degrees of freedoms (DoF) in the system increases. The VE-TFCC approach is benchmarked with small test models and a real molecular compound (CoF4- anion) against the conventional sum over states (SOS) method and applied to calculate thermochemistry properties of a gas-phase reaction: CoF3 + F- → CoF4-. Results shows that the VE-TFCC approach, in conjunction with vibronic models, provides an effective protocol for calculating thermodynamic properties of vibronic coupling systems.

Non-adiabatic Non-axisymmetric Electron-Optic Systems for Multi-mirror and Multi-barrel Gyrotrons

Non-adiabatic Non-axisymmetric Electron-Optic Systems for Multi-mirror and Multi-barrel Gyrotrons

Dynamical transfer behavior and in situ interaction with H2O molecules of charge carriers over heterojunction in non-adiabatic systems

In adiabatic systems, both photocatalytic Z-scheme and S-scheme mechanisms are feasible. However, almost all photocatalysis are non-adiabatic, and the mechanisms need to be rationalized. Herein, CuS was in-situ grown at S locus of MoS2, thus increasing their wave function overlapping to decrease the interface barrier. In situ DRIFTS and XPS, and Hall effect studies have found that Fermi levels are not equal at interfaces in non-adiabatic system, and consequently the internal electric fields are formed at interfaces and localized electric fields in bulk and on surface, which boost e- and h+ to transfer directionally to MoS2 as reductive sites and CuS as oxidative sites for dehydrogenating * -OH and coupling * -O and releasing H2 and O2 with STH efficiency of 1.70%. In-depth insight into charge transfer behavior and dynamical reaction process over heterojunctions in non-adiabatic systems indicates the general validity of photocatalytic models and facilitates rational designs and photocatalysis principle understanding.

A multi-state mapping approach to surface hopping.

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

Electronic-state chaos, intramolecular electronic energy redistribution, and chemical bonding in persisting multidimensional nonadiabatic systems.

We study the chaotic, huge fluctuation of electronic state, resultant intramolecular energy redistribution, and strong chemical bonding surviving the fluctuation with exceedingly long lifetimes of highly excited boron clusters. Those excited states constitute densely quasi-degenerate state manifolds. The huge fluctuation is induced by persisting multidimensional nonadiabatic transitions among the states in the manifold. We clarify the mechanism of their coexistence and its physical significance. In doing so, we concentrate on two theoretical aspects. One is quantum chaos and energy randomization, which are to be directly extracted from the properties of the total electronic wavefunctions. The present dynamical chaos takes place through frequent transitions from adiabatic states to others, thereby making it very rare for the system to find dissociation channels. This phenomenon leads to the concept of what we call intramolecular nonadiabatic electronic-energy redistribution, which is an electronic-state generaliztion of the notion of intramolecular vibrational energy redistribution. The other aspect is about the peculiar chemical bonding. We investigate it with the energy natural orbitals (ENOs) to see what kind of theoretical structures lie behind the huge fluctuation. The ENO energy levels representing the highly excited states under study appear to have four robust layers. We show that the energy layers responsible for chaotic dynamics and those for chemical bonding are widely separated from each other, and only when an event of what we call "inter-layer crossing" happens to burst can the destruction of these robust energy layers occur, resulting in molecular dissociation. This crossing event happens only rarely because of the large energy gaps between the ENO layers. It is shown that the layers of high energy composed of complex-valued ENOs induce the turbulent flow of electrons and electronic-energy in the cluster. In addition, the random and fast time-oscillations of those high energy ENOs serve as a random force on the nuclear dynamics, which can work to prevent a concentration of high nuclear kinetic energy in the dissociation channels.

Observation of modes reversion by encircling exceptional points in high-order non-hermitian system

The special properties of non-trivial topological structures usually come from a so-called edge mode which emerges in the band gap after the band inversion. The topological winding number of exceptional points (EPs) in non-Hermitian physical systems can be regarded as another type of topology. In photonics, the topological properties of EPs have been observed widely both in adiabatic and non-adiabatic second-order non-Hermitian systems. Here, we construct a higher-order non-Hermitian system with meta-atoms, including two independent second-order EPs. By circling EPs in different paths in the Riemann parameter surface, we observe extraordinary modes of reversion and repulsion, which is quite different from the conventional second-order EP systems. We propose a theoretical model of three-resonance non-Hermitian system and verify experimentally the mode reversion by encircling exceptional points in the microwave band, which may pave a new way for studying the topological physical mechanism of non-Hermitian systems, and provide a practical experimental system for its application.

Importance Sampling for Equilibrium Properties in Non-Adiabatic Systems: Application to Anomalous Interfacial Charge Transfer

Interfacial charge transfer plays a significant role in the performance of optoelectronic devices. Compared with real-time non-adiabatic dynamics simulations, statistical mechanics could obtain the equilibrium properties directly. We here present an importance sampling approach to calculate the electron distribution at general interfaces. The configuration distribution based on a series of reference potential energy surfaces is utilized to reweight the properties of interest. The high accuracy, precision, and efficiency of the new method are verified by comparing the results of different sampling approaches and non-adiabatic dynamics simulations. We find that numbers of states, electronic couplings, reorganization energies, and energetic disorders all have strong impacts on the anomalous interfacial charge transfer across a high energy barrier. In addition, based on the data computed by importance sampling in relatively small but diverse systems, we propose an effective machine learning approach to train artificial neural networks, which could predict the interfacial charge transfer in extremely large systems. Due to its high performance, our importance sampling method is promising for the statistical study of equilibrium properties in general non-adiabatic systems.

How "Berry Phase" Analysis of Non-Adiabatic Non-Hermitian Systems Reflects Their Geometry.

There is currently great interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a "phase" parameter that characterises the way "exceptional points" (singularities of various sorts) determine the system. These systems are briefly reviewed here with an emphasis on their geometrical thermodynamics properties.

A new method to measure magnetic nanoparticle heating efficiency in non-adiabatic systems using transient pulse analysis.

Heating magnetic nanoparticles (MNPs) with alternating magnetic fields (AMFs) have applications in biomedical research and cancer therapy. Accurate measurement of the heating efficiency or specific loss power (SLP) generated by the MNPs is essential to assess response(s) in biological systems. Efforts to develop standardized equipment and to harmonize results obtained from various MNP samples and AMF systems have met with little success. Without a standardized magnetic nanoparticle or calorimeter device, objective comparisons of estimated thermal output among laboratories remain a challenge. In addition, the most widely used adiabatic initial slope model fails to account for thermal losses, which are unavoidable. We propose a non-adiabatic method to analyze MNP heating efficiency derived from the Box-Lucas equation, wherein the sample is subjected to several short duration heating pulses. SLP is then estimated from an arithmetic average of the Box-Lucas fitted coefficients obtained from each pulse. Heating experiments were conducted with two identical samples that were placed within vessels having different thermal insulation using the same AMF parameters. Though the samples generated different temperature curves, the pulsed Box-Lucas method produced nearly equivalent SLP estimates. Further, the pulsed test enabled analysis of the heat transfer coefficient providing quantitative measures of sample heat loss throughout the test, with robust statistical confidence. We anticipate this new methodology will aid efforts to standardize measurements of MNP heating efficiency, enabling direct comparison among varied systems.

Nonadiabatic Couplings Can Speed Up Quantum Tunneling Transition Path Times.

Quantum tunneling is known to play an important role in the dynamics of systems with nonadiabatic couplings. However, until recently, the time-domain properties of nonadiabatic scattering have been severely under-explored. Using numerically exact quantum methods, we study the impact that nonadiabatic couplings have on the time it takes to tunnel through a barrier. We find that the Wigner phase time is the appropriate measure to use when determining the tunneling flight time also when considering nonadiabatic systems. The central result of the present study is that in an avoided crossing system in one dimension, the nonadiabatic couplings speed up the tunneling event, relative to the adiabatic case in which all nonadiabatic coupling is ignored. This has implications for both the study of quantum tunneling times and for the field of nonadiabatic scattering and chemistry.

Moving boundary truncated grid method for electronic nonadiabatic dynamics.

The moving boundary truncated grid method is developed to study the wave packet dynamics of electronic nonadiabatic transitions between a pair of diabatic potential energy surfaces. The coupled time-dependent Schrödinger equations (TDSEs) in the diabatic representation are integrated using adaptive truncated grids for both the surfaces. As time evolves, a variable number of grid points fixed in space are activated and deactivated without any advance information of the wave packet dynamics. Essential features of the truncated grid method are first illustrated through applications to three one-dimensional model problems, including the systems of single avoided crossing, dual avoided crossing, and extended coupling region with reflection. As a demonstration for chemical applications, the truncated grid method is then employed to study the dynamics of photoisomerization of retinal in rhodopsin described by a two-electronic-state two-dimensional model. To demonstrate the capability of the truncated grid method to deal with the electronic nonadiabatic problem in high dimensionality, we consider a multidimensional electronic nonadiabatic system in two, three, and four dimensions. The results indicate that the correct grid points are automatically activated to capture the growth and decay of the wave packets on both of the surfaces. Therefore, the truncated grid method greatly decreases the computational effort to integrate the coupled TDSEs for multidimensional electronic nonadiabatic systems.

Ultrafast Internal Conversion Dynamics through the on-the-Fly Simulation of Transient Absorption Pump-Probe Spectra with Different Electronic Structure Methods.

An on-the-fly surface-hopping simulation protocol is developed for the evaluation of transient absorption (TA) pump-probe (PP) signals of molecular systems exhibiting internal conversion to the electronic ground state. We study the nonadiabatic dynamics of azomethane and the associating TA PP spectra at three levels of the electronic-structure theory, OM2/MRCI, SA-CASSCF, and XMS-CASPT2. The impact of these methods on the population dynamics and time-resolved TA PP signals is substantially different. This difference is attributed to the strong non-Condon effects that must be taken into account for the proper understanding and interpretation of time-resolved TA PP signals of nonadiabatic polyatomic systems. This shows that the combination of the dynamical and spectral simulations definitely provides more accurate and detailed information on the microscopic mechanisms of photophysical and photochemical processes. Hence the simulation of time-resolved spectroscopic signals provides another important dimension to examine the accuracy of quantum chemistry methods.

Ab initiononadiabatic dynamics of semiconductor materials via surface hopping method

Photoinduced carrier dynamic processes are without doubt the main driving force responsible for the efficient performance of semiconductor nano-materials in applications like photoconversion and photonics. Nevertheless, establishing theoretical insights into these processes is computationally challenging owing to the multiple factors involved in the processes, namely reaction rate, material surface area, material composition etc. Modelling of photoinduced carrier dynamic processes can be performed via nonadiabatic molecular dynamics (NA-MD) methods, which are methods specifically designed to solve the time-dependent Schrodinger equation with the inclusion of nonadiabatic couplings. Among NA-MD methods, surface hopping methods have been proven to be a mighty tool to mimic the competitive nonadiabatic processes in semiconductor nanomaterials, a worth noticing feature is its exceptional balance between accuracy and computational cost. Consequently, surface hopping is the method of choice for modelling ultrafast dynamics and more complex phenomena like charge separation in Janus transition metal dichalcogenides-based van der Waals heterojunction materials. Covering latest state-of-the-art numerical simulations along with experimental results in the field, this review aims to provide a basic understanding of the tight relation between semiconductor nanomaterials and the proper simulation of their properties via surface hopping methods. Special stress is put on emerging state-ot-the-art techniques. By highlighting the challenge imposed by new materials, we depict emerging creative approaches, including high-level electronic structure methods and NA-MD methods to model nonadiabatic systems with high complexity.

Quantum Wave Packet Treatment of Cold Nonadiabatic Reactive Scattering at the State-To-State Level.

Cold and ultracold collisions are dominated by quantum effects, such as resonances, tunneling, and nonadiabatic transitions between different electronic states. Due to the extremely long de Broglie wavelength in such processes, quantum reactive scattering is most conveniently characterized using the time-independent close-coupling (TICC) methods. However, the TICC approach is difficult for systems with a large number of channels because of its steep numerical scaling laws. Here, a recently proposed quantum wave packet (WP) approach for solving adiabatic reactive scattering problems at low collision energies is extended to include nonadiabatic transitions. To impose the outgoing boundary conditions, the total scattering wavefunction is split into three parts, the interaction, the asymptotic, and the long-range regions. Each region is associated with a different set of basis functions, which could be optimized separately. In this way, an extremely long grid can be used to accommodate the characteristic long de Broglie wavelengths in the scattering coordinate. The better numerical scaling laws of the WP approach have the potential for handling larger nonadiabatic reactive systems at low temperatures in the future.

Unified Formulation of Phase Space Mapping Approaches for Nonadiabatic Quantum Dynamics.

Nonadiabatic dynamical processes are one of the most important quantum mechanical phenomena in chemical, materials, biological, and environmental molecular systems, where the coupling between different electronic states is either inherent in the molecular structure or induced by the (intense) external field. The curse of dimensionality indicates the intractable exponential scaling of calculation effort with system size and restricts the implementation of "numerically exact" approaches for realistic large systems. The phase space formulation of quantum mechanics offers an important theoretical framework for constructing practical approximate trajectory-based methods for quantum dynamics. This Account reviews our recent progress in phase space mapping theory: a unified framework for constructing the mapping Hamiltonian on phase space for coupled F-state systems where the renowned Meyer-Miller Hamiltonian model is a special case, a general phase space formulation of quantum mechanics for nonadiabatic systems where the electronic degrees of freedom are mapped onto constraint space and the nuclear degrees of freedom are mapped onto infinite space, and an isomorphism between the mapping phase space approach for nonadiabatic systems and that for nonequilibrium electron transport processes. While the zero-point-energy parameter is conventionally assumed to be positive, we show that the constraint implied in the conventional Meyer-Miller mapping Hamiltonian requires that such a parameter can be negative as well and lies in (-1/F, +∞) for each electronic degree of freedom. More importantly, the zero-point-energy parameter should be interpreted as a special case of a commutator matrix in the comprehensive phase space mapping Hamiltonian for nonadiabatic systems. From the rigorous formulation of mapping phase space, we propose approximate but practical trajectory-based nonadiabatic dynamics methods. The applications to both gas phase and condensed phase problems include the spin-boson model for condensed phase dissipative two-state systems, the three-state photodissociation models, the seven-site model of the Fenna-Matthews-Olson monomer in photosynthesis of green sulfur bacteria, the strongly coupled molecular/atomic matter-optical cavity systems designed for controlling and manipulating chemical dynamical processes, and the Landauer model for a quantum dot state coupled with two electrodes. In these applications the overall performance of our phase space mapping dynamics approach is superior to two prevailing trajectory-based methods, Ehrenfest dynamics and fewest switches surface hopping.

Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics.

We show that a novel, general phase space mapping Hamiltonian for nonadiabatic systems, which is reminiscent of the renowned Meyer-Miller mapping Hamiltonian, involves a commutator variable matrix rather than the conventional zero-point-energy parameter. In the exact mapping formulation on constraint space for phase space approaches for nonadiabatic dynamics, the general mapping Hamiltonian with commutator variables can be employed to generate approximate trajectory-based dynamics. Various benchmark model tests, which range from gas phase to condensed phase systems, suggest that the overall performance of the general mapping Hamiltonian is better than that of the conventional Meyer-Miller Hamiltonian.

Generalized discrete truncated Wigner approximation for nonadiabatic quantum-classical dynamics.

Nonadiabatic molecular dynamics occur in a wide range of chemical reactions and femtochemistry experiments involving electronically excited states. These dynamics are hard to treat numerically as the system's complexity increases, and it is thus desirable to have accurate yet affordable methods for their simulation. Here, we introduce a linearized semiclassical method, the generalized discrete truncated Wigner approximation (GDTWA), which is well-established in the context of quantum spin lattice systems, into the arena of chemical nonadiabatic systems. In contrast to traditional continuous mapping approaches, e.g., the Meyer-Miller-Stock-Thoss and the spin mappings, GDTWA samples the electron degrees of freedom in a discrete phase space and thus forbids an unphysical unbounded growth of electronic state populations. The discrete sampling also accounts for an effective reduced but non-vanishing zero-point energy without an explicit parameter, which makes it possible to treat the identity operator and other operators on an equal footing. As numerical benchmarks on two linear vibronic coupling models and Tully's models show, GDTWA has a satisfactory accuracy in a wide parameter regime, independent of whether the dynamics is dominated by relaxation or by coherent interactions. Our results suggest that the method can be very adequate to treat challenging nonadiabatic dynamics problems in chemistry and related fields.

Non-adiabatic ring polymer molecular dynamics with spin mapping variables.

We present a new non-adiabatic ring polymer molecular dynamics (NRPMD) method based on the spin mapping formalism, which we refer to as the spin mapping NRPMD (SM-NRPMD) approach. We derive the path-integral partition function expression using the spin coherent state basis for the electronic states and the ring polymer formalism for the nuclear degrees of freedom. This partition function provides an efficient sampling of the quantum statistics. Using the basic properties of the Stratonovich-Weyl transformation, we further justify a Hamiltonian that we propose for the dynamical propagation of the coupled spin mapping variables and the nuclear ring polymer. The accuracy of the SM-NRPMD method is numerically demonstrated by computing the nuclear position and population auto-correlation functions of non-adiabatic model systems. The results obtained using the SM-NRPMD method agree very well with the numerically exact results. The main advantage of using the spin mapping variables over the harmonic oscillator mapping variables is numerically demonstrated, where the former provides nearly time-independent expectation values of physical observables for systems under thermal equilibrium. We also explicitly demonstrate that SM-NRPMD provides invariant dynamics upon various ways of partitioning the state-dependent and state-independent potentials.

Non-adiabatic Matsubara dynamics and non-adiabatic ring-polymer molecular dynamics.

We present the non-adiabatic Matsubara dynamics, a general framework for computing the time-correlation function (TCF) of electronically non-adiabatic systems. This new formalism is derived based on the generalized Kubo-transformed TCF using the Wigner representation for both the nuclear degrees of freedom and the electronic mapping variables. By dropping the non-Matsubara nuclear normal modes in the quantum Liouvillian and explicitly integrating these modes out from the expression of the TCF, we derived the non-adiabatic Matsubara dynamics approach. Further making the approximation to drop the imaginary part of the Matsubara Liouvillian and enforce the nuclear momentum integral to be real, we arrived at the non-adiabatic ring-polymer molecular dynamics (NRPMD) approach. We have further justified the capability of NRPMD for simulating the non-equilibrium TCF. This work provides the rigorous theoretical foundation for several recently proposed state-dependent RPMD approaches and offers a general framework for developing new non-adiabatic quantum dynamics methods in the future.

Investigating the Stability and Accuracy of a Classical Mapping Variable Hamiltonian for Nonadiabatic Quantum Dynamics

Previous work has shown that by using the path integral representation of quantum mechanics and by mapping discrete electronic states to continuous Cartesian variables, it is possible to derive an exact quantum “mapping variable” ring-polymer (MV-RP) Hamiltonian. The classical molecular dynamics generated by this MV-RP Hamiltonian can be used to calculate equilibrium properties of multi-level quantum systems exactly, and to approximate real-time thermal correlation functions (TCFs). Here, we derive mixed time-slicing forms of the MV-RP Hamiltonian where different modes of a multi-level system are quantized to different extents. We explore the accuracy of the approximate quantum dynamics generated by these Hamiltonians through numerical calculation of quantum real-time TCFs for a range of model nonadiabatic systems, where two electronic states are coupled to a single nuclear degree of freedom. Interestingly, we find that the dynamics generated by an MV-RP Hamiltonian with all modes treated classically is more stable across all model systems considered here than mixed quantization approaches. Further, we characterize nonadiabatic dynamics in the 6D phase space of our classical-limit MV-RP Hamiltonian using Lagrangian descriptors to identify stable and unstable manifolds.