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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Pt Nanoparticle Disintegration at Oxide Interfaces Enhances CO Oxidation Catalysis

Understanding how supported metal nanoparticles dynamically evolve under reaction conditions is critical for controlling their catalytic function. Here, the mechanism behind the dynamic disintegration of Pt nanoparticles (NPs) supported on CeOx-TiO2 (CT) during CO oxidation is elucidated, leading to the formation of single atoms (SAs) and/or sub-nanometer clusters. Density functional theory (DFT) calculations reveal that strong Pt-CO interactions weaken Pt─Pt cohesion, while electronic coupling between Pt and Ce ions stabilizes Pt-CO* intermediates at the oxide interface. Surface oxygen vacancies kinetically trap Pt-CO*, but the vacancies are replenished under oxygen-rich conditions, enabling Pt-CO* surface diffusion and subsequent structural reorganization. In situ spectroscopic analyses confirm the oxygen-driven transformation of Pt NPs, correlating with a threefold increase in mass-specific activity at 150 °C. These findings demonstrate that interfacial oxygen dynamics and metal-support interactions can be leveraged to induce nanoparticle disintegration and optimize catalytic performance, highlighting the catalytic potential of interface-engineered Pt nanostructures.

CO oxidation↗
DOE OSTI2022

On the use of vibronic coherence to identify reaction coordinates for ultrafast excited-state dynamics of transition metal-based chromophores

In this study, the question of whether one can use information from quantum coherence as a means of identifying vibrational degrees of freedom that are active along an excited-state reaction coordinate is discussed. Specifically, we are exploring the notion of whether quantum oscillations observed in single-wavelength kinetics data exhibiting coherence dephasing times that are intermediate between that expected for either pure electronic or pure vibrational dephasing are vibronic in nature and therefore may be coupled to electronic state-to-state evolution. In the case of a previously published Fe(ιι) polypyridyl complex, coherences observed subsequent to 1 A 1 → 1 MLCT excitation were linked to large-amplitude motion of a portion of the ligand framework; dephasing times on the order of 200–300 fs suggested that these degrees of freedom could be associated with ultrafast (~100 fs) conversion from the initially formed MLCT excited state to lower-energy, metal-centered ligand-field excited state(s) of the compound. Incorporation of an electronically benign but sterically restrictive Cu(ι) ion into the superstructure designed to interfere with this motion yielded a compound exhibiting a ~25-fold increase in the compound’s MLCT lifetime, a result that was interpreted as confirmation of the initial hypothesis. However, new data acquired on a different chemical system – Cr(acac') 3 (where acac' represents various derivatives of acetylacetonate) – yielded results that call into question this same hypothesis. Coherences observed subsequent to 4 A 2 → 4 T 2 ligand-field excitation on a series of molecules implicated similar vibrational degrees of freedom across the series, but exhibited dephasing times ranging from 340 fs to 2.5 ps without any clear correlation to the dynamics of excited-state evolution in the system. Taken together, the results obtained on both of these chemical platforms suggest that while identification of coherences can indeed point to degrees of freedom that should be considered as candidate modes for defining reaction trajectories, our understanding of the factors that determine the interplay across coherences, dephasing times, and electronic and geometric structure is insufficient at the present time to view this parameter as a robust metric for differentiating active versus spectator modes for ultrafast dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

REACTER: A Heuristic Method for Reactive Molecular Dynamics

REACTER (www.reacter.org) is a heuristic protocol that enables the simulation of complex reactions using atomistic molecular dynamics (MD) with a fixed-valence force field. Incorporating reactions into classical MD with this approach allows modeling of reactive systems over greatly-increased time scales, enabling systems to be modeled with MD that would not otherwise be feasible. One or more competing multi-step reactions or series of reactions can be invoked simultaneously. Special treatment can be applied to neighboring atoms to relax high energy configurations while the simulation progresses. The original version of REACTER, which was implemented in the open-source LAMMPS simulation package as fix bond/react, was only available for serial simulations. This work describes the expansion of fix bond/react for use in parallel simulations, as well as the addition of various new options, including deletion of reaction by-products, reversible reactions, and custom reaction constraints. These new capabilities are demonstrated through large-scale simulations (200,000+ atoms) of the polymerization of polystyrene and nylon 6,6. The morphologies of both polymers are analyzed after reaching >99% extent of polymerization. Finally, the newly-added reversible reactions feature is demonstrated by rupturing these highly-entangled systems under uniaxial strain by defining a chain scission reaction.

polymer simulations, molecular dynamics↗
DOE OSTI2023

Atomic Dynamics of Multi‐Interfacial Migration and Transformations

Redox-induced interconversions of metal oxidation states typically result in multiple phase boundaries that separate chemically and structurally distinct oxides and suboxides. Directly probing such multi-interfacial reactions is challenging because of the difficulty in simultaneously resolving the multiple reaction fronts at the atomic scale. Using the example of CuO reduction in H 2 gas, a reaction pathway of CuO → monoclinic m-Cu 4 O 3 → Cu 2 O is demonstrated and identifies interfacial reaction fronts at the atomic scale, where the Cu 2 O/m-Cu 4 O 3 interface shows a diffuse-type interfacial transformation; while the lateral flow of interfacial ledges appears to control the m-Cu 4 O 3 /CuO transformation. Together with atomistic modeling, it is shown that such a multi-interface transformation results from the surface-reaction-induced formation of oxygen vacancies that diffuse into deeper atomic layers, thereby resulting in the formation of the lower oxides of Cu 2 O and m-Cu 4 O 3 , and activate the interfacial transformations. In conclusion, these results demonstrate the lively dynamics at the reaction fronts of the multiple interfaces and have substantial implications for controlling the microstructure and interphase boundaries by coupling the interplay between the surface reaction dynamics and the resulting mass transport and phase evolution in the subsurface and bulk.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Enhanced Sampling Aided Design of Molecular Photoswitches

Advances in the evolving field of atomistic simulations promise important insights for the design and fundamental understanding of novel molecular photoswitches. Here, in this study, we use state-of-the-art enhanced simulation techniques to unravel the complex, multistep chemistry of donor–acceptor Stenhouse adducts (DASAs). Our reaction discovery workflow consists of enhanced sampling for efficient chemical space exploration, refinement of newly observed pathways with more accurate ab initio electronic structure calculations, and structural modifications to introduce design principles within future generations of DASAs. We showcase our discovery workflow by not only recovering the full photoswitching mechanism of DASA but also predicting a plethora of new plausible thermal pathways and suggesting a way for their experimental validation. Furthermore, we illustrate the tunability of these newly discovered reactions, leading to a potential avenue for controlling DASA dynamics through multiple external stimuli. Overall, these insights could offer alternative routes to increase the efficiency and control of DASA’s photoswitching mechanism, providing new elements to design more complex light-responsive materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Quantitative measurements of reactive oxygen species partitioning in electron transfer flavoenzyme magnetic field sensing

Biological magnetic field sensing that gives rise to physiological responses is of considerable importance in quantum biology. The radical pair mechanism (RPM) is a fundamental quantum process that can explain some of the observed biological magnetic effects. In magnetically sensitive radical pair (RP) reactions, coherent spin dynamics between singlet and triplet pairs are modulated by weak magnetic fields. The resulting singlet and triplet reaction products lead to distinct biological signaling channels and cellular outcomes. A prevalent RP in biology is between flavin semiquinone and superoxide (O 2 •–) in the biological activation of molecular oxygen. This RP can result in a partitioning of reactive oxygen species (ROS) products to form either O 2 •– or hydrogen peroxide (H 2 O 2 ). Here, we examine magnetic sensing of recombinant human electron transfer flavoenzyme (ETF) reoxidation by selectively measuring O 2 •– and H 2 O 2 product distributions. ROS partitioning was observed between two static magnetic fields at 20 nT and 50 μT, with a 13% decrease in H 2 O 2 singlet products and a 10% increase in O 2 •– triplet products relative to 50 µT. RPM product yields were calculated for a realistic flavin/superoxide RP across the range of static magnetic fields, in agreement with experimental results. For a triplet born RP, the RPM also predicts about three times more O 2 •– than H 2 O 2 , with experimental results exhibiting about four time more O 2 •– produced by ETF. The method presented here illustrates the potential of a novel magnetic flavoprotein biological sensor that is directly linked to mitochondria bioenergetics and can be used as a target to study cell physiology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2010

A Flight-Calibrated Methodology for Determination of Cassini Thruster On-Times for Reaction Wheel Biases

The Cassini spacecraft, the largest and most complex interplanetary spacecraft ever built, continues to undertake unique scientific observations of planet Saturn, Titan, Enceladus, and other moons of the ring world. In order to maintain a stable attitude during the course of its mission, this three-axis stabilized spacecraft uses two different control systems: the Reaction Control System (or RCS) and the Reaction Wheel Assembly (RWA) control system. In the course of its mission, Cassini performs numerous reaction wheel momentum biases (or unloads) using its reaction control thrusters. The use of the RCS thrusters often imparts undesired velocity changes (delta Vs) on the spacecraft and it is crucial for Cassini navigation and attitude control teams to be able to, quickly but accurately, predict the hydrazine usage and delta V vector in Earth Mean Equatorial (J2000) inertial coordinates for reaction wheel bias events, without actually having to spend time and resources simulating the event in a dynamic or hardware-in-the-loop simulation environments. The flight-calibrated methodology described in this paper, and the ground software developed thereof, are designed to provide the RCS thruster on-times, with acceptable accuracy and without any form of dynamic simulation, for reaction wheel biases, along with the hydrazine usage and the delta V in EME-2000 inertial frame.

Reaction Control System↗
DOE OSTI2021

Ab initio metadynamics calculations reveal complex interfacial effects in acetic acid deprotonation dynamics

Acid-base reactions play a central role in solution chemistry, with carboxylic acids being particularly important in atmospheric chemical processes. In this work, we harness metadynamics calculations with Born-Oppenheimer molecular dynamics (BOMD) simulations to understand deprotonation dynamics of acetic acid (CH 3 COOH) in both bulk and air-water interfacial environments. Collective variables are carefully chosen in our well-tempered metadynamics simulations to capture the deprotonation process in various aqueous configurations. Herein, our findings show that the free energy barrier for deprotonation of acetic acid at the air-water interface is lower than in the bulk, in accordance with the available experimental data. Furthermore, our well-tempered metadynamics calculations suggest that the variations in free energy are primarily due to intricate solvation shell effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Chemo‐Mechanical Coupling in Hydrogels: Dynamics in the Diffusion‐Limited Regime

Hydrogels are characterized by substantial volume changes in response to external stimuli, making them promising candidates for developing smart materials with enhanced adaptability and responsiveness. By integrating chemical reactions, hydrogels acquire dynamic and tunable responsiveness to external stimuli through chemo‐mechanical coupling, expanding their potential in emerging applications. However, capturing their transient behavior remains challenging due to the complex interplay of chemical reactions, solvent transport, and polymer network deformation. Classical theories capture equilibrium swelling but fail to describe time‐dependent phenomena. To address this, a time‐dependent continuum model is developed that explicitly couples these processes. Volume phase transition in hydrogels with homogeneous chemical reactions is investigated, then the effects of reaction kinetics on these transitions are analyzed. The coupling of these mechanisms is further explored through a study of transient mechanical instabilities. To illustrate the impact of distinct reaction and diffusion timescales, a photo‐active gripper is studied for robotic applications. Finally, a photo‐active microswimmer that exhibits non‐reciprocal motion is proposed to highlight the solvent diffusion for locomotion at the micro‐ and nano‐ scales. The work establishes that transient dynamics of chemo‐mechanical hydrogels generate functions not accessible by steady state models and provides a predictive platform for designing adaptive materials in emerging applications.

chemo-mechanical coupling↗
DOE OSTI2021

Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics

Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process and correctly calculating the relative free energies of different polymorphs. Here, we demonstrate, for the prototypical case of urea nucleation from the melt, how one can learn such a one-dimensional reaction coordinate as a function of prespecified order parameters and use it to perform efficient biased all-atom molecular dynamics simulations. The reaction coordinate is learnt as a function of the generic thermodynamic and structural order parameters using the “spectral gap optimization of order parameters (SGOOP)” approach [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. U.S.A. (2016)] and is biased using well-tempered metadynamics simulations. The reaction coordinate gives insights into the role played by different structural and thermodynamics order parameters, and the biased simulations obtain accurate relative free energies for different polymorphs. This includes an accurate prediction of the approximate pressure at which urea undergoes a phase transition and one of the metastable polymorphs becomes the most stable conformation. Here, we believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, generic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1983

ECUT: Energy Conversion and Utilization Technologies program. Heterogeneous catalysis modeling program concept

Insufficient theoretical definition of heterogeneous catalysts is the major difficulty confronting industrial suppliers who seek catalyst systems which are more active, selective, and stable than those currently available. In contrast, progress was made in tailoring homogeneous catalysts to specific reactions because more is known about the reaction intermediates promoted and/or stabilized by these catalysts during the course of reaction. However, modeling heterogeneous catalysts on a microscopic scale requires compiling and verifying complex information on reaction intermediates and pathways. This can be achieved by adapting homogeneous catalyzed reaction intermediate species, applying theoretical quantum chemistry and computer technology, and developing a better understanding of heterogeneous catalyst system environments. Research in microscopic reaction modeling is now at a stage where computer modeling, supported by physical experimental verification, could provide information about the dynamics of the reactions that will lead to designing supported catalysts with improved selectivity and stability.

Voecks, G. E.↗
DOE OSTI2020

A statistical model for the product energy distribution in reactions leading to prompt dissociation

Direct dynamics calculations have been performed for three reactions: C 3 H 8 + H → i-C 3 H 7 + H 2 , C 3 H 8 + H → n-C 3 H 7 + H 2 , and C 2 H 3 + O 2 → HCO + CH 2 O. The fraction of the population for the radical products that promptly dissociates is computed. Here the results for C 3 H 8 + H are qualitatively similar to previous results for C 3 H 8 + OH, but the new results exhibit a slightly higher branching fraction for prompt dissociation products, owing to the fact that a greater fraction of the internal energy in the transition state ends up in the radical. For C 2 H 3 + O 2 → HCO + CH 2 O, the fraction of HCO that promptly dissociates is in excess of 99%. Consequently, the main product for C 2 H 3 + O 2 at lower temperatures should be written as H + CO + CH 2 O and not HCO + CH 2 O. These results are then compared with four previous systems: CH 2 O + H → HCO + H 2 , CH 2 O + OH → HCO + H 2 O, C 3 H 8 + OH → i-C 3 H 7 + H 2 O, and C 3 H 8 + OH → n-C 3 H 7 + H 2 O. Based upon these seven system, several statistical models are presented. The goal of these statistical models is to predict the fraction of the transition state energy that ends up in the rovibrationally excited radical. On average, these statistical models provide an excellent prediction of product energy distribution. Consequently, these models can be used instead of costly trajectory simulations for predicting prompt radical dissociation for larger species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Challenges in the study of chemistry and photochemistry at air–water interfaces: Toward in situ monitoring of reaction kinetics with spectroscopic techniques

Air–water interfaces, including those on droplet surfaces, have been the subject of many recent experiments due to their propensity for unique chemistry. Here, in this study, an overview of some recent advancements in understanding interfacial reaction kinetics is provided, highlighting non-surface-specific methods—such as mass spectrometry—compared with the advantages of surface-specific techniques—such as reflection–absorption spectroscopy, sum frequency generation, and photoelectron spectroscopy. This Perspective discusses the information depth and time constraints of common surface-specific spectroscopic methods that need to be addressed to monitor interfacial chemistry in situ and uses a few key examples from the literature as case studies. It concludes by advocating for the continued development of advanced spectroscopic methods to further investigate interfacial chemistry, underscoring the need for interdisciplinary collaboration to bridge the gap between molecular-level insights and macroscopic observations in future research.

Air-water interface↗
DOE OSTI2025

Reward based optimization of resonance-enhanced piezoresponse spectroscopy

Dynamic spectroscopies in scanning probe microscopy (SPM) are critical for probing material properties, such as force interactions, mechanical properties, polarization switching, electrochemical reactions, and ionic dynamics. However, the practical implementation of these measurements is constrained by the need to balance imaging time and data quality. Signal to noise requirements favor long acquisition times and high frequencies to improve signal fidelity. However, these are limited on the low end by contact resonant frequency and photodiode sensitivity and on the high end by the time needed to acquire high-resolution spectra or the propensity for sample degradation under high field excitation over long times. The interdependence of key parameters such as instrument settings, acquisition times, and sampling rates makes manual tuning labor-intensive and highly dependent on user expertise, often yielding operator-dependent results. These limitations are prominent in techniques like dual amplitude resonance tracking in piezoresponse force microscopy that utilize multiple concurrent feedback loops for topography and resonance frequency tracking. Here, a reward-driven workflow is proposed that automates the tuning process, adapting experimental conditions in real time to optimize data quality. Furthermore, this approach significantly reduces the complexity and time required for manual adjustments and can be extended to other SPM spectroscopic methods, enhancing overall efficiency and reproducibility.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

River Dynamics Control Transit Time Distributions and Biogeochemical Reactions in a Dam-Regulated River Corridor

Residence Time Distributions (RTDs) exert an important control on biogeochemical translation in the hydrological systems. Previous tracer studies have revealed that RTDs often followed time-invariant exponential, lognormal, or heavy-tailed RTDs that have power-law behavior for long tails in headwater or low-order streams. However, there is a recognition that RTDs can be more complicated and time-variable in response to dynamic hydrological forcing. Here, we use particle tracking to estimate RTDs along the Hanford Reach of the Columbia River and to quantify the influences of river stage fluctuations. Particle tracking is conducted using the velocity field from high-resolution 3D groundwater flow simulations. The effects of hydrological forcing on the residence time distribution were evaluated by varying river flow boundary conditions and releasing particles in different time windows. Our results revealed that dynamic stage fluctuations created rapidly changing losing-gaining conditions in the river and led to highly transient RTDs, which contributes to multiple modes of RTDs. Dam-induced high-frequency (sub-daily) flow variation contributes to the short-time (sub-daily) component of the RTDs. Deviation of the reactant consumption under the single-mode assumption compared to the multimodal RTDs is relatively small (~5%) and appears when the Damköhler number was close to one.More specifically, high-frequency (daily) dam-induced stage variations have higher impacts on biogeochemical reactions with faster reaction rate, and can potentially increase the reactant consumption by 26.68%. Based on these findings, we suggest that current river basin models could be improved by including bank storage and more complex RTDs influenced by both short and long term river stage fluctuations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Assessment of the impact of reactor residence time distribution on non-equilibrium product selectivity of polypropylene pyrolysis using reactive molecular dynamics simulations

Mass residence time distribution (RTD) is considered to be an important factor controlling the product selectivity in the pyrolysis of biomass and plastic wastes along with the pyrolysis chemistry. However, due to the complex pyrolysis chemistry of biomass and plastic waste, the coupling between the reaction chemistry, RTD, and product selectivity is challenging to understand. Here, we introduce a reaction molecular dynamics-based method to examine pyrolysis chemistry and species timescales to assess the impact of RTD on product selectivity and yield. To validate this method, reactive molecular dynamics simulations were conducted for polypropylene pyrolysis and its non-equilibrium product selectivity using 6 different RTDs. We find that the RTD and the reaction chemistry control the peak non-equilibrium product concentrations. The peak monomer (C 3 H 6 ) concentration during pyrolysis can be increased by up to 25 % by using a narrow RTD in the case of polypropylene pyrolysis. We also find that product selectivity is strongly affected by the average residence time and RTD. This coupling between the reaction chemistry, RTD, and product selectivity highlights the need to understand detailed reaction chemistry to control RTD and optimize non-equilibrium product selectivity during polymer and biomass pyrolysis. The present method provides a new way to design RTD for reactors to reach maximized product selectivity of plastic waste and biomass.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS2010

A Flight-Calibrated Methodology for Determination of Cassini Thruster On-Times for Reaction Wheel Biases

This paper describes a methodology for accurate and flight-calibrated determination of the on-times of the Cassini spacecraft Reaction Control System (RCS) thrusters, without any form of dynamic simulation, for the reaction wheel biases. The hydrazine usage and the delta V vector in body frame are also computed from the respective thruster on-times. The Cassini spacecraft, the largest and most complex interplanetary spacecraft ever built, continues to undertake ambitious and unique scientific observations of planet Saturn, Titan, Enceladus, and other moons of Saturn. In order to maintain a stable attitude during the course of its mission, this three-axis stabilized spacecraft uses two different control systems: the RCS and the reaction wheel assembly control system. The RCS is used to execute a commanded spacecraft slew, to maintain three-axis attitude control, control spacecraft's attitude while performing science observations with coarse pointing requirements, e.g. during targeted low-altitude Titan and Enceladus flybys, bias the momentum of reaction wheels, and to perform RCS-based orbit trim maneuvers. The use of RCS often imparts undesired delta V on the spacecraft. The Cassini navigation team requires accurate predictions of the delta V in spacecraft coordinates and inertial frame resulting from slews using RCS thrusters and more importantly from reaction wheel bias events. It is crucial for the Cassini spacecraft attitude control and navigation teams to be able to, quickly but accurately, predict the hydrazine usage and delta V for various reaction wheel bias events without actually having to spend time and resources simulating the event in flight software-based dynamic simulation or hardware-in-the-loop simulation environments. The methodology described in this paper, and the ground software developed thereof, are designed to provide just that. This methodology assumes a priori knowledge of thrust magnitudes and thruster pulse rise and tail-off time constants for eight individual attitude control thrusters, the spacecraft's wet mass and its center of mass location, and a few other key parameters.

Earth Mean Equatorial↗
DOE OSTI2023

Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by the property of being fully-coherent: the algorithm succeeds with arbitrarily high success probability 1 − δ while only requiring a single copy of the initial state. Here we subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time t, ln(1/δ), and ln(1/ϵ) for error tolerance ϵ: $Θ‖\mathscr{H}‖|t|+ln(1/ϵ)+ln(1/δ)$. Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H2 molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves as a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗