Engineering PapersSearch

SEARCH · Engineering Papers

Results for “master equation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

Infrared Fingerprint and Unimolecular Decay Dynamics of the Hydroperoxyalkyl Intermediate (•QOOH) in Cyclopentane Oxidation

A transient carbon-centered hydroperoxyalkyl intermediate (•QOOH) in the oxidation of cyclopentane is identified by IR action spectroscopy with time-resolved unimolecular decay to hydroxyl (OH) radical products that are detected by UV laser-induced fluorescence. Two nearly degenerate •QOOH isomers, β- and γ-QOOH, are generated by H atom abstraction of the cyclopentyl hydroperoxide precursor. Fundamental and first overtone OH stretch transitions and combination bands of •QOOH are observed and compared with anharmonic frequencies computed by second-order vibrational perturbation theory. An OH stretch transition is also observed for a conformer arising from torsion about a low-energy CCOO barrier. Definitive identification of the β-QOOH isomer relies on its significantly lower transition state (TS) barrier to OH products, which results in rapid unimolecular decay and near unity branching to OH products. A benchmarking approach is utilized to compute high-accuracy stationary point energies, most importantly TS barriers, for cyclopentane oxidation (C 5 H 9 O 2 ), building on higher level reference calculations for ethane oxidation (C 2 H 5 O 2 ). The experimental OH product appearance rates are compared with computed statistical microcanonical rates using RRKM theory, including heavy-atom tunneling, thereby validating the computed TS barrier. The results are extended to thermal unimolecular decay rate constants at temperatures and pressures relevant to cyclopentane combustion via master-equation modeling. Furthermore, the various torsional and ring puckering states of the wells and transition states are explicitly considered in these calculations.

Chemical calculations

Rate constants and third-body collision efficiencies for recombination of Na with OH and O2: Implications for flame inhibition by alkali salts

Flame inhibition by alkali metals has implications for solid fuel combustion, fire safety, and a number of industrial processes. While the mechanism of inhibition is fairly well understood, details related to thermodynamic properties and rate constants are still in question. In the present work, the recombination of Na with OH (R5) and O2 (R7), respectively, was characterized theoretically, and the implications for modeling laminar premixed hydrogen flames doped with sodium species were examined. Third-body collision efficiencies and low-pressure-limit rate constants were obtained using newly fitted ab initio-based potential energy surfaces, classical trajectories, and one-dimensional master equation calculations. The results are consistent with available experimental results and aid in the present modeling study by providing rate information for bath gases and conditions that remain unexplored experimentally. Chemical kinetic modeling of relative Na and absolute H and OH profiles in H2-fueled laminar, premixed flames doped with a sodium salt shows that the most important radical removal cycle is the sequence Na + OH (+M) → NaOH (+M) (R5), NaOH + H → Na + H2O (R12), even under oxidizing conditions. A secondary cycle, Na + O2 (+M) ⇄ NaO2 (+M) (R7), NaO2 + OH → NaOH + O2 (R14), is less important due to the low thermal stability of NaO2. In most flames, reaction R7 is partially equilibrated, and reaction R14 becomes rate-limiting for the second cycle. The flame analysis supports a lower value of k14 than indicated by recent work on KO2 + OH, but more work is required to confirm this.

Jasper, Ahren W.

Kinetics and Mechanism of the Singlet Oxygen Atom Reaction with Dimethyl Ether

Here, we combine in situ laser spectroscopy, quantum chemistry, and kinetic calculations to study the reaction of a singlet oxygen atom with dimethyl ether. Infrared laser absorption spectroscopy and Faraday rotation spectroscopy are used for the detection and quantification of the reaction products OH, H 2 O, HO 2 , and CH 2 O on submillisecond time scales. Fitting temporal profiles of products with simulations using an in-house reaction mechanism allows product branching to be quantified at 30, 60, and 150 Torr. The experimentally determined product branching agrees well with master equation calculations based on electronic structure data and transition state theory. The calculations demonstrate that the dimethyl peroxide (CH 3 OOCH 3 ) generated via O-insertion into the C–O bond undergoes subsequent dissociation to CH 3 O + CH 3 O through energetically favored reactions without an intrinsic barrier. This O-insertion mechanism can be important for understanding the fate of biofuels leaking into the atmosphere and for plasma-based biofuel processing technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Interplay between Ultrafast Electronic and Librational Dynamics in Liquid Nitrobenzene Probed with Two-Color Four-Wave Mixing

Here, we present an experimental and theoretical study of the interplay between ultrafast electron dynamics and librational dynamics in liquid nitrobenzene. A femtosecond ultraviolet pulse and two femtosecond near-infrared pulses interact with nitrobenzene molecules, generating a four-wave mixing nonlinear signal measured in the Optical Kerr Effect geometry. The signal is measured to be nonzero only at negative time delays, corresponding to the near-infrared pulses arriving before the ultraviolet pulse. We perform time-dependent Quantum Master Equation calculations with classical libration to simulate the experiment. The simulations support the conclusion that the near-infrared pulses launch librational motion while creating electronic coherences resulting in a libration-modulated electronic nonlinear response. The analysis of the phase-matched four-wave mixing signals suggests a nonparametric process leaving the molecules in an excited electronic state, providing new insight into ultrafast nonlinear optical interactions in liquids and advancing toward probing ultrafast electronic coherences in complex molecular liquids.

Shivaram, Niranjan [Lawrence Berkeley National Lab

Predictive Chemical Kinetic Modeling: Where We Succeed, Where We Struggle, and What Comes Next

Chemical kinetic modeling plays a foundational role in fields ranging from energy to environmental science, pharmaceuticals, and advanced materials. The past two decades have seen remarkable progress, particularly in modeling gas-phase reactions for thermochemical processes, leading to impactful industrial applications such as steam cracking and air quality management. However, new challenges are emerging. The successful development of systematic methodologies for the description of gas-phase kinetics opens the possibility to apply the same approach to the study of more challenging systems. Here, we review recent advances, including ab initio transition state theory-based master equation estimation of elementary rates, automated mechanism generation, machine-learning-assisted kinetics, and uncertainty quantification, and discuss the advances needed to apply the same methodological approach in areas such as heterogeneous catalysis, electrochemistry, liquid-phase and solid-state reactivity, and multiscale model integration. We advocate for the development of targeted tools, especially methods that go beyond empirical tuning toward first-principles-based predictions. We highlight the need for accessible software and AIaugmented workflows to democratize modeling for industry and academia alike. In this perspective, we call attention to not only what has worked but also what remains unsolved, advocating to avoid overemphasizing successes in scientific works at the expense of realism. The next decade should focus on predictive capability, physical accuracy, and community infrastructure (e.g., databases and services) to enable innovation across diverse fields. We argue that kinetic modeling, properly equipped, can accelerate discovery far beyond its traditional domains.

ab initio calculations

Chemistry of Sugar Formation in the Gas Phase: Following the Activated Aldehyde

Sugars are produced by living organisms, and are required building blocks for life as we know it, which raises the foundational question of how sugars formed in a prebiotic environment. The abiotic formose reaction produces sugars from formaldehyde, but our understanding of its initiation step remains murky, with chemists invoking the concept of an “activated aldehyde” to seed this reaction. Singlet hydroxycarbenes, high-energy isomers of aldehydes, were recently reported to facilitate sugar formation under cold, nonaqueous conditions relevant to interstellar environments. Here, we generate singlet methylhydroxycarbene ( 1 CH 3 –C̈–OH) from the photodissociation of pyruvic acid and experimentally measure its gas-phase reaction with d 4 -acetaldehyde using multiplexed photoionization mass spectrometry. The C 4 H 4 D 4 O 2 isomer d 4 -acetoin is the sole product, which we kinetically link to the reactant CH 3 –C̈–OH, and attribute to a carbonyl-ene formation mechanism. We see no evidence of 3-hydroxybutanal, the C–H insertion product expected in carbene chemistry. Using automated exploration we calculate stationary points on the potential energy surface and report master equation rate coefficients from T = 20–600 K, providing quantitative kinetics of this fast reaction for use in chemical models. The prereactive complex in this reaction is stabilized by both hydrogen bonding and electrophilic carbene C═O interactions. These effects create a short-range dynamical bottleneck for the reaction besides the long- and midrange barrierless bottlenecks. Combined with recent reports of 1 HC̈OH production from methanol photodissociation and pyruvic acid production in cold irradiated ices, this work provides evidence that singlet hydroxycarbene + aldehyde chemistry is a feasible path to prebiotic sugar formation.

aldehydes

Theoretical analysis of the OH-initiated atmospheric oxidation reactions of imidazole

Imidazoles are present in Earth's atmosphere in both the gas-phase and in aerosol particles, and have been implicated in the formation of brown carbon aerosols. The gas-phase oxidation of imidazole (C 3 N 2 H 4 ) by hydroxyl radicals has been shown to be preferentially initiated via OH-addition to position C5, producing the 5-hydroxyimidazolyl radical adduct. However, the fate of this adduct upon reaction with O 2 in the atmospheric gas-phase is currently unknown. We employed an automated approach to investigate the reaction mechanism and kinetics of imidazole's OH-initiated gas-phase oxidation, in the presence of O 2 and NO x . The explored mechanism included reactions available to first-generation RO 2 radicals, as well as alkoxyl radicals produced from RO 2 + NO reactions. Product distributions were obtained by assembling and solving a master equation, under conditions relevant to the Earth's atmosphere. Our calculations show a complex, branched reaction mechanism, which nevertheless converges to yield two major closed-shell products: 4H-imidazol-4-ol (4H-4ol) and N,N′-diformylformamidine (FMF). At 298 K and 1 atm, we estimate the yields of 4H-4ol and FMF from imidazole oxidation initiated via OH-addition to position C5 to be 34 : 66, 12 : 85 and 2 : 95 under 10 ppt, 100 ppt and 1 ppb of NO respectively. This work also revealed O 2 -migration pathways between the α-N-imino peroxyl radical isomers. This reaction channel is fast for the first-generation RO 2 radicals, and may be important during the atmospheric oxidation of other unsaturated organic nitrogen compounds as well.

Almeida, Thomas Golin

Direct measurements for the kinetics of C–C bond fission in the high temperature decomposition of isopropanol

The thermal decomposition of isopropanol was studied experimentally and theoretically with a view to isolate and directly measure rate coefficients for the dominant radical channel in this multi-channel process. Two complementary shock tube methods, laser schlieren densitomtery and H-atom atomic resonance absorption spectroscopy, were used to obtain rate coefficents for the C–C bond fission channel. The experimental ranges span temperatures from 1200–2100 K and pressures between 30–690 torr. These are the most direct measurements of this rate coefficent in the fall-off regime of relevance to high-temperature reacting systems. Theoretical studies also performed in this work confirm that the title reaction and a molecular elimination involving dehydration were the sole unimolecular processes at high temperatures. A master equation analysis yielded k ( T, P ) for the C–C fission and these are shown to be in good agreement with the present experimental measurements. Comparisons with prior experimental and theoretical studies in the literature indicate branching ratios as well as absolute k ( T, P ) for C–C bond-fission have been under-predicted for this decomposition reaction. Consequently, results from the present studies place an increased emphasis on radical-driven secondary processes in high-temperature pyrolysis of this simplest secondary alcohol.

Kim, John H. [Univ. of Michigan, Ann Arbor, MI (Un

Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Non-equilibrium rate theory for polariton relaxation dynamics

We derive an analytic expression of the non-equilibrium Fermi’s golden rule (NE-FGR) expression for a Holstein–Tavis–Cumming Hamiltonian, a universal model for many molecules collectively coupled to the optical cavity. These NE-FGR expressions capture the full-time-dependent behavior of the rate constant for transitions from polariton states to dark states. The rate is shown to be reduced to the well-known frequency domain-based equilibrium Fermi’s golden rule (E-FGR) expression in the equilibrium and collective limit and is shown to retain the same scaling with the number of sites in non-equilibrium and non-collective cases. We use these NE-FGR to perform population dynamics with a time-non-local and time-local quantum master equation and obtain accurate population dynamics from the initially occupied upper or lower polariton states. Furthermore, NE-FGR significantly improves the accuracy of the population dynamics when starting from the lower polariton compared to the E-FGR theory, highlighting the importance of the non-Markovian behavior and the short-time transient behavior in the transition rate constant.

Chemical dynamics

Molecular axis distribution moments in ultrafast transient absorption spectroscopy: A path toward ultrafast quantum state tomography

In ultrafast time-resolved experiments with gas phase molecules, the alignment of the molecular axis relative to the polarization of the interacting laser pulses plays a crucial role in determining the dynamics following this light–matter interaction. The molecular axis distribution is influenced by the interacting pulses and is intrinsically linked to the electronic coherences of the excited molecules. However, in typical theoretical calculations of such interactions, the signal is either calculated for a single molecule in the molecular frame or averaged over all possible molecular orientations to compare with the experiment. Such averaging removes information about anisotropy in the molecular-axis distribution, even though anisotropic contributions can play a significant role in the measured experimental signal. Here, we calculate the laboratory frame transient electronic first-order polarization [P (1) ] spectra in terms of separated molecular frame and laboratory frame quantities. The laboratory frame polarizations are compared with orientation-averaged quantum master equation calculations, demonstrating that orientation-averaging captures only the isotropic contributions. We show that our formalism also allows us to evaluate the anisotropic contributions to the spectrum. Lastly, we discuss the application of this approach to achieve ultrafast quantum state tomography using transient absorption spectroscopy and field observables in nonlinear spectroscopy.

74 ATOMIC AND MOLECULAR PHYSICS

The origin of the Stokes–Einstein relation in simple dense liquids

Here, we investigate the origin of the universal relation between structural relaxation and diffusion in simple dense liquids, known as the Stokes–Einstein (SE) relation. The fact that this relation, originally derived from a hydrodynamic model of a macroscopic particle in a viscous medium, can describe the microscopic-scale liquid dynamics still eludes understanding. We introduce a new universal measure of structural relaxation in a system of N identical particles based on an explicit decomposition of the configuration space into N! congruent convex polyhedra. This measure makes it possible to quantify the correlation between two distinct particle configurations in terms of their minimal Euclidean distance, optimized with respect to particle permutations. Using this measure alongside a model of independent random walkers under the single-occupancy constraint, we derive a master equation that quantifies the SE relation. It allows us to demonstrate that the universal relation between structural relaxation and diffusion in simple dense liquids is caused by two conditions: (a) the confinement of the dominant density fluctuations to the first coordination shell, manifested by de Gennes narrowing, and (b) Gaussianity of the diffusion process; the former is shown to be violated in low-density fluids, and the latter is known to be violated in supercooled liquids.

Physics - Condensed matter physics

General framework for quantifying dissipation pathways in open quantum systems. III. Off-diagonal subsystem–bath couplings

This paper extends the previously reported theory of dissipation pathways [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111 (2024)] to incorporate off-diagonal subsystem–bath coupling, which is often required to model molecular systems where the environment directly influences transitions and couplings between subsystem states. We systematically derive master equations for both population transfer and dissipation into individual bath components, for which we also rigorously prove energy conservation and detailed balance. The approach is based on second-order perturbation theory with respect to the subsystem–bath couplings, whose form is not limited to any specific model. The accuracy of the developed method is tested by applying it to diverse model Hamiltonians involving linearly coupled harmonic oscillator baths and comparing the outcomes against the hierarchical equations of motion (HEOM) method. Overall, our method accurately quantifies the contributions of specific bath components to the overall dissipation while significantly reducing the computational cost compared to numerically exact methods such as HEOM, thus offering a path to examine how vibronic interactions steer non-adiabatic processes in realistic chemical systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Transient hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation. I. Conformer- and isomer-resolved infrared spectra

Transient carbon-centered hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation are characterized by infrared (IR) action spectroscopy under jet-cooled conditions with selective detection of hydroxyl (OH) radical products. Two distinct •QOOH isomers with radical sites at a primary carbon of one of the methyl groups (β-Me) or a secondary carbon (β-Et) of the ethyl group are identified by comparison with theoretically calculated IR absorption features for multiple conformers, including C–O, ethyl, and O–O torsions of the two isomers. Here, a master-equation analysis is developed and utilized to explore the conformational cooling process and the resultant conformer population distributions of the two isomers. Most of the IR features observed, including those in the strong fundamental and first overtone OH stretch regions as well as weaker combination bands involving OH stretch with torsion or OOH bend, are in good accord with computed anharmonic frequencies for the most populated conformers of the •QOOH_Et isomer. Relatively weak IR features most evident in the fundamental and first overtone OH stretch regions are ascribed to multiple conformers of the less stable •QOOH_Me isomer, along with a weak feature that is uniquely attributed to a combination band involving asymmetric CH 2 stretch and HCH bend of •QOOH_Me.

Chemical reaction jet spectroscopy

Decoherence and Brownian motion of a polarizable particle near a medium

Optically levitated nanoparticles are ideal experimental testbeds for investigating macroscopic superpositions and microscopic thermodynamics. Integrating such levitated nanoparticles with photonic structures can enable strong coupling between their center-of-mass motion and guided photonic modes, facilitating enhanced control and probing of their motion. When coupling a particle to a photonic structure, such as a waveguide, the effects of fluctuations become prominent at nanoscales. In this work, we analyze the classical and quantized center-of-mass motion of a polarizable particle interacting with the fluctuations of the electromagnetic field in the presence of a medium. We derive a position localization master equation for the particle's quantized center of mass, and examine its classical center-of-mass momentum diffusion, elucidating correspondences between classical and quantum Brownian motion of polarizable particles near media. We study the decoherence rate of the particle in the presence of a planar surface as a function of temperature and distance from the surface, comparing it to common sources of decoherence. Our results are pertinent to experiments aimed at preparing levitated nanospheres in macroscopic quantum states and investigating their Brownian dynamics.

Brownian motion

Gauge-fixing quantum density operators at scale

We provide a theory, algorithms, and simulations of nonequilibrium quantum systems using a one-dimensional (1D) completely positive (CP), matrix-product (MP) density-operator (𝜌) representation. By generalizing the matrix product state's orthogonality center, to additionally store positive classical mixture correlations, the MP⁢𝜌 factorization naturally emerges. In this setting, we analytically and numerically examine the virtual gauge freedoms associated with the representation of quantum density operators. Based on this perspective, we simplify algorithms in certain limits to speed up the integration of the canonical-form master-equation dynamics. This enables us to quickly evolve under the dynamics of two-body quantum channels without resorting to optimization-based methods. In addition to this technical advance, we also scale up numerical examples and discuss implications for accurately modeling hardware architectures and predicting their performance in the near term. This includes an example of the quantum to classical transition of informationally leaky, i.e., decohering, qubits. In this setting, because of loss from environmental interactions, nonlocal complex coherence correlations are converted into global incoherent classical statistical mixture correlations. Lastly, the representation of both global and local correlations is discussed. We expect this work to have applications in additional nonequilibrium settings, beyond qubit engineering.

Gangapuram, Amit Jamadagni [Oak Ridge National Lab

Auxiliary-state-facilitated phase synchronization phenomena in isolated spin systems

Extending classical synchronization to the quantum domain is of great interest both from the fundamental physics point of view and with a view toward quantum technology applications. This work characterizes phase synchronization of an effective spin-1 system, which is realized by coupling three quantum states with infinite lifetime to auxiliary excited states that have a finite lifetime. Integrating out the excited states, the effective spin-1 model features coherent and incoherent effective couplings. The following are our key findings. (i) Phase synchronization can be controlled by adjusting the phases of the couplings to the excited states. (ii) Unlike in the paradigmatic spin-1 system studied in the literature, where the dissipative couplings describe decay into the limit-cycle state, the effective spin-1 model investigated in this work is governed by a competition between dissipative decay into and out of the limit-cycle state, with the dissipative decay out of the limit-cycle state playing a critical role. (iii) We identify a parameter regime where phase synchronization of the effective spin-1 system is, in the absence of coherent effective couplings, governed entirely by the effective dissipators. The effective spin-1 model is benchmarked through comparisons with master-equation calculations for the full Hilbert space. Physical insights are gained through analytical perturbation theory calculations. In conclusion, our findings, which are expected to hold for a broad class of energy-level and coupling schemes, are examined using hyperfine states of 87 Rb as an example system.

Nonlinear optics