Nonadiabatic Processes Research Articles

Structure, Seebeck coefficient and DC electrical conductivity of Bi2Mn4O10 prepared by mechanochemical method

Bismuth and manganese oxides were mixed as source-materials using the mechanochemical technique followed by heat treatment to prepare the phase Bi2Mn4O10. The X-Ray Diffraction (XRD) analysis was carried out to obtain the formed phases during the mechanochemical process. Bismuth manganese oxide phase with the chemical formula Bi2Mn4O10 was formed at heat treatment 1073 K and was partially decomposed to γ-Bi12.8O19.2 and α-Mn2O3 after 5 h of milling time. The variation of the crystallite size is obtained at different milling time (1 h, 5 h, 10 h, 15 h, 30 h and 50 h). The temperature dependency of the DC electrical conductivity was observed at different milling times in the temperature range 300–425 K for the samples milled at 5 h, 10 h, 30 h and 50 h. The temperature dependency (300–4 80 K) of the thermoelectric power/Seebeck coefficient (S) and its modulus variation with milling time were observed; the modulus varied in the range (45 µV/K-277 µV/K). The concentration of manganese ions (N), the average distance between manganese ions (R) and the fraction (C) of reduced transition ions were calculated for all samples. The hopping carrier mobility (μ) of the samples was also calculated at a fixed temperature. As a result, the conduction mechanism agreed with the non-adiabatic process of small polaron hopping.

Differential Cross Sections for Cold, State-to-State Spin-Orbit Changing Collisions of NO(v = 10) with Neon.

Inelastic scattering processes have proven a powerful means of investigating molecular interactions, and much current effort is focused on the cold and ultracold regime where quantum phenomena are clearly manifested. Studies of collisions of the open shell nitric oxide (NO) molecule have been central in this effort since the pioneering work of Houston and co-workers in the early 1990s. State-to-state scattering of vibrationally excited molecules in the cold regime introduces challenges that test the suitability of current theoretical methods for ab initio determination of intermolecular potentials, and concomitant electronically nonadiabatic processes raise the bar further. Here we report measurements of differential cross sections for state-to-state spin-orbit changing collisions of NO (v = 10, Ω″ = 1.5, and j″ = 1.5) with neon from 2.3 to 3.5 cm-1 collision energy using our recently developed near-copropagating beam technique. The experimental results are compared with those obtained from quantum scattering calculations on a high-level set of coupled cluster potential energy surfaces and are shown to be in good agreement. The theoretical results suggest that distinct backscattering in the 2.3 cm-1 case arises from overlapping resonances.

Describing the photo-isomerization of a retinal chromophore model with coupled and quantum trajectories.

The exact factorization of the electron-nuclear wavefunction is applied to the study of photo-isomerization of a retinal chromophore model. We describe such an ultrafast nonadiabatic process by analyzing the time-dependent potentials of the theory and by mimicking nuclear dynamics with quantum and coupled trajectories. The time-dependent vector and scalar potentials are the signature of the exact factorization, as they guide nuclear dynamics by encoding the complete electronic dynamics and including excited-state effects. Analysis of the potentials is, thus, essential-when possible-to predict the time-dependent behavior of the system of interest. In this work, we employ the exact time-dependent potentials, available for the numerically exactly solvable model used here, to propagate quantum nuclear trajectories representing the isomerization reaction of the retinal chromophore. The quantum trajectories are the best possible trajectory-based description of the reaction when using the exact-factorization formalism and, thus, allow us to assess the performance of the coupled-trajectory, fully approximate schemes derived from the exact-factorization equations.

Stereodynamics-Controlled Product Branching in the Nonadiabatic H + NaD → Na(3s, 3p) + HD Reaction at Low Temperatures.

Nonadiabatic processes play an important role at energies near or higher than conical intersection of adiabatic potential energy surfaces in chemical reactions. In this work, dynamics of the nonadiabatic H + NaD reaction at low temperatures are studied by using the quantum wave packet method based on an improved L-shaped grid. The nonadiabatic H + NaD reaction has two exothermic reaction channels: Na(3s) + HD and Na(3p) + HD; the latter can only occur via nonadiabatic transition. The dynamics results show that the product branching of the H + NaD reaction at collision energies ranging from 20 to 80 cm-1 is controlled by stereodynamics. The Na(3s) and Na(3p) reaction channels occur through collinear collision and side-on collision, respectively. When the collision energy is lower than 20 cm-1, the resonance-mediated reaction mechanism is dominant in both the Na(3s) and Na(3p) reaction channels.

Theoretical perspectives on non-Born-Oppenheimer effects in chemistry.

The Born-Oppenheimer approximation, which assumes that the electrons respond instantaneously to the motion of the nuclei, breaks down for a wide range of chemical and biological processes. The rate constants of such nonadiabatic processes can be calculated using analytical theories, and the real-time nonequilibrium dynamics can be described using numerical atomistic simulations. The selection of an approach depends on the desired balance between accuracy and efficiency. The computational expense of generating potential energy surfaces on-the-fly often favours the use of approximate, robust and efficient methods such as trajectory surface hopping for large, complex systems. The development of formally exact non-Born-Oppenheimer methods and the exploration of well-defined approximations to such methods are critical for providing benchmarks and preparing for the next generation of faster computers. Thus, the parallel development of rigorous but computationally expensive methods and more approximate but computationally efficient methods is optimal. This Perspective briefly summarizes the available theoretical and computational non-Born-Oppenheimer methods and presents examples illustrating how analytical theories and nonadiabatic dynamics simulations can elucidate the fundamental principles of chemical and biological processes. These examples also highlight how theoretical calculations are able to guide the interpretation of experimental data and provide experimentally testable predictions for nonadiabatic processes. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Generalized Ab Initio Nonadiabatic Dynamics Simulation Methods from Molecular to Extended Systems.

Nonadiabatic dynamics simulation has become a powerful tool to describe nonadiabatic effects involved in photophysical processes and photochemical reactions. In the past decade, our group has developed generalized trajectory-based ab initio surface-hopping (GTSH) dynamics simulation methods, which can be used to describe a series of nonadiabatic processes, such as internal conversion, intersystem crossing, excitation energy transfer and charge transfer of molecular systems, and photoinduced nonadiabatic carrier dynamics of extended systems with and without spin-orbit couplings. In this contribution, we will first give a brief introduction to our recently developed methods and related numerical implementations at different computational levels. Later, we will present some of our latest applications in realistic systems, which cover organic molecules, biological proteins, organometallic compounds, periodic organic and inorganic materials, etc. Final discussion is given to challenges and outlooks of ab initio nonadiabatic dynamics simulations.

The invariant-based shortcut to adiabaticity for qubit heat engine operates under quantum Otto cycle

In this paper, we study the role and relevance of the cost for an invariant-based shortcut to adiabaticity enabled qubit heat engine operates in a quantum Otto cycle. We consider a qubit heat engine with Landau-Zener Hamiltonian and improve its performance using the Lewis–Riesenfeld invariant-based shortcut to adiabaticity method. Addressing the importance of cost for better performance, the paper explores its relationship with the work and efficiency of the heat engine. We analyze the cost variation with the time duration of non-adiabatic unitary processes involved in the heat engine cycle. The cost required to attain the quasi-static performance of the qubit heat engine is also discussed. We found the efficiency lost due to non-adiabaticity of the engine can be revived using the shortcut method and it is even possible to attain quasi-static performance under finite time with higher cost.

NAST: Nonadiabatic Statistical Theory Package for Predicting Kinetics of Spin-Dependent Processes.

We present a nonadiabatic statistical theory (NAST) package for predicting kinetics of spin-dependent processes, such as intersystem crossings, spin-forbidden unimolecular reactions, and spin crossovers. The NAST package can calculate the probabilities and rates of transitions between the electronic states of different spin multiplicities. Both the microcanonical (energy-dependent) and canonical (temperature-dependent) rate constants can be obtained. Quantum effects, including tunneling, zero-point vibrational energy, and reaction path interference, can be accounted for. In the limit of an adiabatic unimolecular reaction proceeding on a single electronic state, NAST reduces to the traditional transition state theory. Because NAST requires molecular properties at only a few points on potential energy surfaces, it can be applied to large molecular systems, used with accurate high-level electronic structure methods, and employed to study slow nonadiabatic processes. The essential NAST input data include the nuclear Hessian at the reactant minimum, as well as the nuclear Hessians, energy gradients, and spin-orbit coupling at the minimum energy crossing point (MECP) between two states. The additional computational tools included in the NAST package can be used to extract the required input data from the output files of electronic structure packages, calculate the effective Hessian at the MECP, and fit the reaction coordinate for more advanced NAST calculations. We describe the theory, its implementation, and three examples of application to different molecular systems.

Accurate description of the nonadiabatic proton-coupled electron-transfer process in a diabatic representation: A model study

Using a two-dimensional model system for the proton-coupled electron-transfer process, the eigenvalues and nonadiabatic dynamics have been notably investigated by means of diabatic representation in the Born-Oppenheimer picture. Different from a previously reported diabatic model, which was approximately determined by the eigenstates of the differently defined electronic Hamiltonians, the rigorous diabatization was achieved by a fitting method based on the adiabatic energies and derivative couplings. As expected, the rigorous diabatic models were found to be able to accurately reproduce the eigenvalues or nonadiabatic dynamics in the adiabatic representation for three different models. Furthermore, we proposed an approximate diabatic scheme, which was built from fitting the adiabatic energies solely but with a fixed form for the off-diagonal terms in the diabatic potential energy matrix. This approximate diabatic model without the aid of the derivative coupling is shown to be as accurate as the rigorous one, which provides a simple and efficient way to accurately describe the complex proton-coupled electron-transfer processes due to accurately computing derivative couplings that are quite challenging for realistic systems.

Solvated Nuclear-Electronic Orbital Structure and Dynamics.

Nonadiabatic dynamical processes such as proton-coupled electron transfer and excited state intramolecular proton transfer have been the subject of much research. One of the promising theoretical methods to describe these processes is the nuclear-electronic orbital (NEO) approach. This approach inherently accounts for nuclear quantum effects within quantum chemistry calculations, and it has recently been extended to directly simulate nonadiabatic processes with the development of real-time NEO methods. These processes can also be significantly dependent on the surrounding chemical environment, however, and capturing the effects of the environment is often necessary for analyzing experimentally relevant systems. This work couples the NEO density functional theory and real-time time-dependent density functional theory approaches with solvation through the polarizable continuum model. The effects of this coupling are investigated for ground state properties, solvent-dependent vibrational frequencies, and direct excited state intramolecular proton transfer dynamics.

A Photochemical Reaction in Different Theoretical Representations

The Born–Oppenheimer picture has forged our representation and interpretation of photochemical processes, from photoexcitation down to the passage through a conical intersection, a funnel connecting different electronic states. In this work, we analyze a full in silico photochemical experiment, from the explicit electronic excitation by a laser pulse to the formation of photoproducts following a nonradiative decay through a conical intersection, by contrasting the picture offered by Born–Oppenheimer and that proposed by the exact factorization. The exact factorization offers an alternative understanding of photochemistry that does not rely on concepts such as electronic states, nonadiabatic couplings, and conical intersections. On the basis of nonadiabatic quantum dynamics performed for a two-state 2D model system, this work allows us to compare Born–Oppenheimer and exact factorization for (i) an explicit photoexcitation with and without the Condon approximation, (ii) the passage of a nuclear wavepacket through a conical intersection, (iii) the formation of excited stationary states in the Franck–Condon region, and (iv) the use of classical and quantum trajectories in the exact factorization picture to capture nonadiabatic processes triggered by a laser pulse.

Diabatic States of Molecules.

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

A multiple time step algorithm for trajectory surface hopping simulations.

A multiple time step (MTS) algorithm for trajectory surface hopping molecular dynamics has been developed, implemented, and tested. The MTS scheme is an extension of the ab initio implementation for Born-Oppenheimer molecular dynamics presented in the work of Liberatore et al. [J. Chem. Theory Comput. 14, 2834 (2018)]. In particular, the MTS algorithm has been modified to enable the simulation of non-adiabatic processes with the trajectory surface hopping (TSH) method and Tully's fewest switches algorithm. The specificities of the implementation lie in the combination of Landau-Zener and Tully's transition probabilities during the inner MTS time steps. The new MTS-TSH method is applied successfully to the photorelaxation of protonated formaldimine, showing that the important characteristics of the process are recovered by the MTS algorithm. A computational speed-up between 1.5 and 3 has been obtained compared to standard TSH simulations, which is close to the ideal values that could be obtained with the computational settings considered.

Recent Advances in the Development of Highly Conductive Structured Supports for the Intensification of Non-adiabatic Gas-Solid Catalytic Processes: The Methane Steam Reforming Case Study

Structured catalysts are strong candidates for the intensification of non-adiabatic gas-solid catalytic processes thanks to their superior heat and mass transfer properties combined with low pressure drops. In the past two decades, different types of substrates have been proposed, including honeycomb monoliths, open-cell foams and, more recently, periodic open cellular structures produced by additive manufacturing methods. Among others, thermally conductive metallic cellular substrates have been extensively tested in heat-transfer limited exo- or endo-thermic processes in tubular reactors, demonstrating significant potential for process intensification. The catalytic activation of these geometries is critical: on one hand, these structures can be washcoated with a thin layer of catalytic active phase, but the resulting catalyst inventory is limited. More recently, an alternative approach has been proposed, which relies on packing the cavities of the metallic matrix with catalyst pellets. In this paper, an up-to-date overview of the aforementioned topics will be provided. After a brief introduction concerning the concept of structured catalysts based on highly conductive supports, specific attention will be devoted to the most recent advances in their manufacturing and in their catalytic activation. Finally, the application to the methane steam reforming process will be presented as a relevant case study of process intensification. The results from a comparison of three different reactor layouts (i.e. conventional packed bed, washcoated copper foams and packed copper foams) will highlight the benefits for the overall reformer performance resulting from the adoption of highly conductive structured internals.

Time-resolved X-ray and XUV based spectroscopic methods for nonadiabatic processes in photochemistry.

The photochemistry of numerous molecular systems is influenced by conical intersections (CIs). These omnipresent nonadiabatic phenomena provide ultra-fast radiationless relaxation channels by creating degeneracies between electronic states and decide over the final photoproducts. In their presence, the Born-Oppenheimer approximation breaks down, and the timescales of the electron and nuclear dynamics become comparable. Due to the ultra-fast dynamics and the complex interplay between nuclear and electronic degrees of freedom, the direct experimental observation of nonadiabatic processes close to CIs remains challenging. In this article, we give a theoretical perspective on novel spectroscopic techniques capable of observing clear signatures of CIs. We discuss methods that are based on ultra-short laser pulses in the extreme ultraviolet and X-ray regime, as their spectral and temporal resolution allow for resolving the ultra-fast dynamics near CIs.

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.

Tracking Conical Intersections with Nonlinear X-ray Raman Spectroscopy

Conical intersections are formed when 2 or more electronic states become degenerate and give rise to ultrafast nonadiabatic processes such as radiation-less decay channels and geometric phase effects. The branching of nuclear wave packets near a conical intersection creates a coherent superposition of electronic states, which carries information about the energy difference of the involved states. X-ray Raman techniques have been proposed to observe the coherent superposition of the electronic states and to monitor the evolving electronic state separation. However, these techniques rely on the coherence generated as the wave packet passes through the conical intersection, and the electronic energy gap before the wave packet passes through the conical intersection is not tracked. In this paper, we theoretically demonstrate how a nonlinear Raman detection scheme can be used to gain further insight into the nonadiabatic dynamics in the vicinity of the conical intersection. We employ a combination of a resonant visible/infrared pulse and an off-resonant x-ray Raman probe to map the electronic state separation around the conical intersection. We demonstrate that this technique can achieve high contrast and is able to selectively probe the narrow electronic state separation around the conical intersection.

General Rules Governing the Dynamical Encircling of an Arbitrary Number of Exceptional Points.

Dynamically encircling an exceptional point in non-Hermitian systems has drawn great attention recently, since a nonadiabatic transition process can occur and lead to intriguing phenomena and applications such as the asymmetric switching of modes. While all previous experiments have been restricted to two-state systems, the dynamics in multistate systems where more complex topology can be formed by exceptional points, is still unknown and associated experiments remain elusive. Here, we propose an on-chip photonic system in which an arbitrary number of exceptional points can be encircled dynamically. We reveal in experiment a robust state-switching rule for multistate systems, and extend it to an infinite-period system in which an exceptional line is encircled with outcomes being located at the Brillouin-zone boundary. The proposed versatile platform is expected to reveal more physics related to multiple exceptional points and exceptional lines, and give rise to applications in multistate non-Hermitian systems.

Tracking the Ionization Site in Neutral Molecules.

When a diatomic molecule is exposed to intense light, the valence electron may tunnel from a higher potential (corresponding to an upfield atom) due to the suppressed internuclear barrier. This process is known as ionization enhancement and is a key mechanism in strong field ionization of molecules. Alternatively, the bound electron wave function can evolve adiabatically in the laser field, resulting in ionization from the downfield atom. Here, we introduce a method to quantify the relative contribution of these two processes. Applying this method to experimentally measured electron momenta distributions following strong field ionization of N_{2} with infrared laser light, we find approximately a 2∶1 ratio of electrons ionized from a downfield atom, relative to upfield. This suggests that the bound state wave function largely adapts adiabatically to the changing laser field, although the nonadiabatic process of ionization enhancement still contributes even in neutral molecules. Our method can be applied to any diatomic neutral molecule to better understand the evolution of the initially bound electron wave packet and hence the nature of the molecular ionization process.

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.