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All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Experimental and theoretical examples of the value and limitations of transition state theory

Value and limitations of transition-state theory (TST) are reviewed. TST analyses of the temperature dependence of the 'direct' reactions CH3 + CH3CHO yields CH4 + CH3CO(1) and O + CH4 yields OH + CH3(2) are presented in detail, and other examples of TST usefulness are recalled. Limitations are discussed for bimolecular processes in terms of 'complex' vs. 'direct' mechanisms. The reaction OH + CO yields CO2 + H is discussed in this context. Limitations for unimolecular processes seem to arise only for simple bond fission processes, and recent advances are noted.

Golden, D. M.↗
DOE OSTI2025

Semiclassical transition state theory through the lens of the restricted partition function

The wide adoption of transition state theory in resolving the rates of molecular processes relies on the simplification from reducing the formal and numerical expense of dynamics by a geometric constraint. Such a reduction is at odds with the uncertainty in localization that the uncertainty principle requires. While many forms of semiclassical transition state theory (SCTST) have been aimed at addressing this challenge, a popular approach has relied on resolving the underlying phase space structure of the exact rate formula to leverage Bohr–Sommerfeld quantization. Here, the Hernandez–Miller SCTST reframed the thermal rate formula into an integral of the so-called restricted partition function (RPF) over the action associated with the reaction. The density-of-state SCTST has reframed the rate formula in terms of the instanton’s density of states (DoS). Here, we show the relationship between the RPF-SCTST and the DoS-SCTST and derive the latter from the former. In this way, we help unify these branches of SCTST and provide a clearer formalism for future advances.

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

Microscopic Derivation of Transition-state Theory for Complex Quantum Systems

The decay of quantum complex systems through a potential barrier is often described with transition-state theory, also known as RRKM theory in chemistry. Here we derive the basic formula for transition-state theory based on a generic Hamiltonian as might be constructed in a configuration-interaction basis. Two reservoirs of random Hamiltonians from Gaussian orthogonal ensembles are coupled to intermediate states representing the transition states at a barrier. Under the condition that the decay of the reservoirs to open channels is large, an analytic formula for reaction rates is derived. Here, the transition states act as independent Breit–Wigner resonances which contribute additively to the total transition probability, as is well known for electronic conductance through resonant tunneling states. It is also found that the transition probability is independent of the decay properties of the states in the second reservoir over a wide range of decay widths.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Restricted Partition Function Semiclassical Transition State Theory (RPF-SCTST): Applications to Reactions Involving Hydrogen Cyanide, Hydrogen Peroxide, and Formaldehyde Oxide

We demonstrate the efficiency of the numerical calculation of thermal semiclassical transition state theory (SCTST) rates across several representative chemical reactions using the restricted partition function (RPF)─viz a function that depends only on the imaginary action associated with a reaction. Here, we treat the potential energy surfaces (PESs) through fourth order expansions around the saddle point and integrate the Hamiltonian up to second order in employing vibrational perturbation theory. We apply this formalism to uni- and bimolecular reactions with different─though relatively high─barrier heights to uncover the influence of the barrier properties, minimal energies, and separability of the rotational motion on rate constants and tunneling corrections. Although all modes are coupled within the RPF, we found in our numerical examples that the rotational component in the absence of significant rotational distortions can be separated from the vibrational contributions. Moreover, a classical treatment of the rotational contribution is adequate over the temperature range from approximately 100 to 1000 K. We also found that the choice of DFT basis set can lead to variations in rate constants of up to an order of magnitude. Lastly, different schemes for counting eligible energy levels result in rate constants that differ by no more than a factor of 2, with the remaining discrepancies attributed to the treatment of near-convergent levels in perturbation theory.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Association of Cl with C 2 H 2 by unified variable-reaction-coordinate and reaction-path variational transition-state theory

Significance A key issue in chemical kinetics is advancing the theoretical framework to handle reactions beyond the domain of textbook transition-state theory by including––for example––anharmonicity, barrierless transition states, transition states in series, and the effect of conformational flexibility on equilibrium constants. Other key issues are validating affordable electronic structure methods for direct dynamics and the direct calculation of high-pressure limiting rate constants, which are often obtainable experimentally only by extrapolation. The present article addresses all these issues for a prototype radical–molecule association reaction and thereby demonstrates how to combine improved theoretical methods to provide rate constants in cases where experimental data are uncertain or missing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Quantum and anharmonic effects in non-adiabatic transition state theory

Quantitative descriptions of non-adiabatic transition rates at intermediate temperatures are challenging due to the simultaneous importance of quantum and anharmonic effects. Here, in this paper, the interplay between quantum effects—for motion across or along the seam of crossing—and anharmonicity in the seam potential is considered within the weak coupling limit. The well-known expression for quantized 1-D motion across the seam (i.e., tunneling) in the linear terms approximation is derived in the thermal domain using the Lagrangian formalism, which is then applied to the case when tunneling is distributed along the seam of crossing (treating motion along the seam classically). For high-frequency quantum modes, a vibrationally adiabatic (VA) approach is developed that introduces to the non-adiabatic rate constant a factor associated with high-frequency wavefunction overlap; this approach treats the high-frequency motion along the seam quantum mechanically. To test these methodologies, the reaction N 2 O ↔ N 2 + O( 3 P) was chosen. CCSD(T)-F12b/cc-pVTZ-F12 explorations of the 3 A'- 1 A' seam of N 2 O revealed that seam anharmonicity has a strong effect on the rate constant (a factor of ~20 at 2000 K). Several quantum effects were found to be significant at intermediate/lower temperatures, including the quantum N–N vibration that was coupled with seam anharmonicity using the VA approach. Finally, a 1-D approximation to non-adiabatic instanton theory is presented to estimate the validity limit of the linear terms model at low temperatures (⁠~ 250 K for N 2 O). We recommend that the assumptions built into many statistical theories for non-adiabatic reactions—harmonic behavior, classical motion, linear terms, and weak coupling—should be verified on a case-by-case basis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Degree of rate control and De Donder relations – An interpretation based on transition state theory

We describe sensitivities of elementary steps as salient parameters in determining the rate determining character of elementary steps within a reaction network and develop a formalism wherein the overall composite reaction is described by an apparent rate-determining step that is a sensitivity-weighted average of the elementary steps that comprise the reaction. Reaction parameters—apparent reaction orders, apparent enthalpy and entropy of activation—of the composite reaction network are determined within the framework we develop by application of transition state theory to the apparent rate-determining step. From this formalism we develop methods for determination of surface coverages by measuring only reaction orders, novel methods for discrimination between proposed mechanisms, a proof that the kinetic degrees of rate control sum to unity, and a proof for the relationship between fractional coverages and thermodynamic degrees of rate control. Two complementary formalisms for identifying rate-limiting transition states are broadly employed in chemical kinetics—De Donder relations based on measuring the thermodynamic driving forces of elementary steps during reaction and degrees of rate control based on knowledge of the kinetics of elementary reaction steps. Here, the formalism developed herein unifies these two strategies to elucidate in the most general case a relationship between the thermodynamic driving forces of elementary steps captured by the reversibilities and the kinetic and thermodynamic degrees of rate control.

42 ENGINEERING↗
DOE OSTI2023

Automated reaction kinetics and network exploration (Arkane): A statistical mechanics, thermodynamics, transition state theory, and master equation software

The open-source statistical mechanics software described here, Arkane–Automated Reaction Kinetics and Network Exploration–facilitates computations of thermodynamic properties of chemical species, high-pressure limit reaction rate coefficients, and pressure-dependent rate coefficient over multi-well molecular potential energy surfaces (PES) including the effects of collisional energy transfer on phenomenological kinetics. Arkane can use estimates to fill in information for molecules or reactions where quantum chemistry information is missing. The software solves the internal energy master equation for complex unimolecular reaction systems. Inputs to the software include converged electronic structure computations performed by the user using a variety of supported software packages (Gaussian, Molpro, Orca, TeraChem, Q-Chem, Psi4). The software outputs high-pressure limit rate coefficients and pressure-dependent phenomenological rate coefficients, as well as computed thermodynamic properties (enthalpy, entropy, and constant pressure heat capacity) with added energy corrections. Some of the key features of Arkane include treatment of 1D, 2D or ND hindered internal rotation modes, treatment of free internal rotation modes, quantum tunneling effect consideration, transition state theory (TST) and Rice-Ramsperger-Kassel-Marcus (RRKM) rate coefficient computations, master equation solution with four implemented methods, inverse-Laplace transform of high-pressure limit rate coefficients into the energy domain, energy corrections based on bond-additivity or isodesmic reactions, automated and efficient PES exploration, and PES sensitivity analysis. The present work describes the design of Arkane, how it should be used, and refers to the theory that it employs. Arkane is distributed via the RMG-Py software suite (https://github.com/ReactionMechanismGenerator/RMG-Py).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1991

Use of scaled external correlation, a double many-body expansion, and variational transition state theory to calibrate a potential energy surface for FH2

New ab initio results and a double many-body expansion formalism have been used to parameterize a new FH2 potential energy surface with improved properties near the saddle point and in the region of long-range attraction. The functional form of the new surface includes dispersion forces by a double many-body expansion. Stationary point properties for the new surface are calculated along with the product-valley barrier maxima of vibrationally adiabatic potential curves for F + H2 - HF(nu-prime = 3) + H, F + HD - HF(nu-prime = 3) + D, and F + D2 - DF(nu-prime = 4) + D. The new surface should prove useful for studying the effect on dynamics of a low, early barrier with a wide, flat bend potential.

Lynch, Gillian C.↗
DOE OSTI2024

Dynamics of HCN, HNC, and HNCO Formation in the 193 nm Photodissociation of Formamide

Formamide (NH 2 CHO) is the simplest molecule containing a peptide linkage [-NH-C($=$O)-], and it plays an essential role in the study of prebiotic chemistry. Exposure to UV irradiation allows formamide to decompose and act as a prebiotic feedstock in the formation of nucleobases and other necessary starting materials. The photodissociation mechanism of gaseous formamide at 193 nm is studied using (a) chirped-pulse Fourier transform millimeter-wave spectroscopy in the 260-290 GHz spectral region in a room-temperature flow-tube reactor at 1 mu bar pressure, (b) a combination of electronic structure theory, transition state theory, and quasiclassical trajectories, and (c) the Active Thermochemical Tables. The HCN and HNC photoproducts of hydrogenated (NH 2 CHO) and deuterated (NH 2 CDO and ND 2 CHO) formamide precursors are examined to gain insight into the photodissociation mechanism. Here, the theoretical investigation has characterized the main pathway leading to each of the HCN/HNC isomers from the precursor isotopologues. The theoretical branching ratio [HNC]/[HCN] = 2.1 for nascent photofragments agrees with the experiment. The effect of the postphotolysis HNC ↔ HCN isomerization on the [HNC]/[HCN] ratio is predicted. We report the experimental branching ratio [HNCO]: ([HNC] + [HCN]) = 12 ± 3 and propose that most of HNCO originates from dissociation on the S-1 electronic state of formamide.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Fullerene Negative Ions: Formation and Catalysis

We first explore negative-ion formation in fullerenes C 44 to C 136 through low-energy electron elastic scattering total cross sections calculations using our Regge-pole methodology. Then, the formed negative ions C 44 – to C 136 – are used to investigate the catalysis of water oxidation to peroxide and water synthesis from H 2 and O 2 . The exploited fundamental mechanism underlying negative-ion catalysis involves hydrogen bond strength-weakening/breaking in the transition state. Density Functional Theory transition state calculations found C 60 – optimal for both water and peroxide synthesis, C 100 – increases the energy barrier the most, and C 136 – the most effective catalyst in both water synthesis and oxidation to H 2 O 2 .

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

Product specific thermal degradation kinetics of bisphenol F epoxy in inert and oxidative atmospheres using evolved gas analysis–mass spectrometry

Knowledge of the degradation kinetics for polymer materials is important for understanding thermal stability. In this study, evolved gas analysis–mass spectrometry and pyrolysis gas-chromatography-mass spectrometry were evaluated for the potential to deliver additional insight into thermal degradation kinetics of diglycidal ether of bisphenol F (DGEBF) epoxy thermoset under inert and oxidative atmospheres. Degradation products of selected precursor ions were evaluated for their uniqueness to the specific precursor using extracted ion thermographs. Unique mass peaks, solely attributed to a single reaction pathway of a specific product, were determined from extracted ion thermographs and used to determine both activation energy (E a ) and pre-exponential factors for the specific primary reaction pathways. These primary reaction pathways for DGEBF epoxy degradation were then evaluated in the context of transition state theory (TST) and related transition state enthalpies (ΔH ‡ ) and entropies (ΔS ‡ ) of activation to further elucidate the degradation process. It was determined under pyrolysis conditions, as suggested by the E a , the formation of bisphenol F monomer was the rate-limiting step toward the formation of xanthene and phenol. In contrast, under thermo-oxidative conditions, reactions involving oxygen containing species were identified as the rate-limiting step for all observed products based on the large negative ΔS ‡ calculated from TST. This work demonstrates a powerful combination of technique and theory that can provide new insight into the degradation of polymer materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Pilgrim : A thermal rate constant calculator and a chemical kinetics simulator

Pilgrim is a program written in Python and designed to use direct dynamics in the calculation of thermal rate constants of chemical reactions by the variational transition state theory (VTST), based on electronic structure calculations for the potential energy surface. Pilgrim can also simulate reaction mechanisms using kinetic Monte Carlo (KMC). For reaction processes with many elementary steps, the rate constant of each of these steps can be calculated by means of conventional transition state theory (TST) or by using VTST. In the current version, Pilgrim can evaluate thermal rates using the canonical version of reaction-path VTST, which requires the calculation of the minimum energy path (MEP) associated with each elementary step or transition structure. Multi-dimensional quantum effects can be incorporated through the small-curvature tunneling (SCT) approximation. These methodologies are available both for reactions involving a single structure of the reactants and the transition state and also for reactions involving flexible molecules with multiple conformations of the reactant and/or of the transition state. For systems with many conformers, the program can evaluate each of the elementary reaction rate constants by multipath canonical VTST or multi-structural VTST. Moreover, the reactant can be unimolecular or bimolecular. Torsional anharmonicity can be incorporated through either the MSTor or the Q2DTor programs. Dual-level calculations are also available in Pilgrim: automatic high-level single-point energies can be used to correct the energy of reactants, transition states, products, and MEP points using the interpolated single-point energies (ISPE) algorithm. When the rate constants of all the chemical processes of interest are known, by means of their calculation using Pilgrim or alternatively through analytical fits to the rate constants as functions of temperature, it is possible to simulate a multistep mechanism under specified laboratory conditions using KMC. Finally, this algorithm allows performing a kinetic simulation to monitor the evolution of each chemical species with time and obtain the product yields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

On the origin of ground-state vacuum-field catalysis: Equilibrium consideration

Recent experiments suggest that vibrational strong coupling (VSC) may significantly modify ground-state chemical reactions and their rates even without external pumping. The intrinsic mechanism of this “vacuum-field catalysis” remains largely unclear. Generally, modifications of thermal reactions in the ground electronic states can be caused by equilibrium or non-equilibrium effects. The former are associated with modifications of the reactant equilibrium distribution as expressed by the transition state theory of chemical reaction rates, while the latter stem from the dynamics of reaching and leaving transition state configurations. In this work, we examine how VSC can affect chemical reactions rates in a cavity environment according to transition state theory. Our approach is to examine the effect of coupling to cavity mode(s) on the potential of mean force (PMF) associated with the reaction coordinate. Within the context of classical nuclei and classical photons and also assuming no charge overlap between molecules, we find that while the PMF can be affected by the cavity environment, this effect is negligible for the usual micron-length cavities used to examine VSC situations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

TUMME: Tsinghua University Minnesota Master Equation program

We report that TUMME is a program for assembling and solving master equations for gas-phase chemical kinetics based on chemically significant eigenmodes. TUMME has interfaces to the Gaussian, Polyrate, and/or MSTor output files that allow the master equation code to obtain the microcanonical flux coefficients needed for the coefficient matrix of the master equation. The flux coefficients for reactions with barriers can be calculated by multi-structural variational transition state theory with small-curvature tunneling (MS-VTST/SCT) or by simpler approximations to this such as conventional transition state theory without tunneling (also called RRKM theory). The flux coefficients for barrierless reactions are provided by a hard-sphere model. TUMME is written in double precision with Python 3; quadruple and octuple precision are also available for some subtasks in C++. The Python code can run in serial or parallel (MP or MPI), and the C++ code can run on a single processor or on multiple processors with OpenMP.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Association Kinetics for Perfluorinated n -Alkyl Radicals

Radical-radical reaction channels are important in the pyrolysis and oxidation chemistry of perfluoroalkyl substances (PFAS). In particular, unimolecular dissociation reactions within unbranched n-perfluoroalkyl chains, and their corresponding reverse barrierless association reactions, are expected to be significant contributors to the gas-phase thermal decomposition of families of species such as perfluorinated carboxylic acids and perfluorinated sulfonic acids. Unfortunately, experimental data for these reactions are scarce and uncertain. Furthermore, obtaining reliable theoretical predictions for such reactions is a laborious and computationally intensive task. Here, in this work, the chemical kinetics of the various association/decomposition reactions producing/decomposing the C 2 -C 4 series of unbranched n-perfluoroalkanes (C 2 F 6 , C 3 F 8 , and C 4 F 10 ) are examined using state-of-the-art ab initio transition-state-theory-based master-equation calculations. The variable-reaction-coordinate transition-state theory (VRC-TST) formalism is employed in computing the microcanonical and canonical rates for the association reactions. Reaction thermochemistry is obtained via composite quantum chemistry calculations and the laddering of error-canceling reaction schemes via a connectivity-based hierarchy approach employing ANL1/ANL0-style reference energies. Lennard-Jones collision model parameters for the considered systems were estimated by a direct dynamics approach, and collisional energy transfer parameters were obtained from analogies to systems of similar size and heavy-atom connectivity. A one-dimensional master equation approach was used to convert the microcanonical rate coefficients from the VRC-TST analysis into temperature- and pressure-dependent rate constants for the association reactions and the reverse dissociation reactions. The data are reported in standardized formats for usage in comprehensive chemical kinetic models for PFAS thermal destruction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Unimolecular Reactions of E -Glycolaldehyde Oxide and Its Reactions with One and Two Water Molecules

The kinetics of Criegee intermediates are important for atmospheric modeling. However, the quantitative kinetics of Criegee intermediates are still very limited, especially for those with hydroxy groups. Here, we calculate rate constants for the unimolecular reaction of E-glycolaldehyde oxide [E-hydroxyethanal oxide, E-(CH 2 OH)CHOO], for its reactions with H 2 O and (H 2 O) 2 , and for the reaction of the E-(CH 2 OH)CHOO…H 2 O complex with H 2 O. For the highest level of electronic structure, we use W3X-L//CCSD(T)-F12a/cc-pVDZ-F12 for the unimolecular reaction and the reaction with water and W3X-L//DF-CCSD(T)-F12b/jun-cc-pVDZ for the reaction with 2 water molecules. For the dynamics, we use a dual-level strategy that combines conventional transition state theory with the highest level of electronic structure and multistructural canonical variational transition state theory with small-curvature tunneling with a validated density functional for the electronic structure. This dynamical treatment includes high-frequency anharmonicity, torsional anharmonicity, recrossing effects, and tunneling. We find that the unimolecular reaction of E-(CH 2 OH)CHOO depends on both temperature and pressure. The calculated results show that E-(CH 2 OH)CHOO…H 2 O + H 2 O is the dominant entrance channel, while previous investigations only considered Criegee intermediates + (H 2 O) 2 . In addition, we find that the atmospheric lifetime of E-(CH 2 OH)CHOO with respect to 2 water molecules is particularly short with a value of 1.71 × 10 –6 s at 0 km, which is about 2 orders of magnitude shorter than those usually assumed for Criegee intermediate reactions with water dimer. We also find that the OH group in E-(CH 2 OH)CHOO enhances its reactivity.

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

An Ab initio based OH initiated oxidation kinetics of glycerol carbonate: A promising biofuel component

The global energy demand is steadily increasing because of the population explosion and economic growth. Fossil fuels supply around 85 % of global primary energy demand. On one hand, fulfilling the increasing energy demands is a big challenge for the next few decades. On the other hand, the continued burning of fossil fuels leads to higher CO2 emissions, severely impacting global warming. Therefore, the policymakers vow to shift from conventional fuels to renewable resources for economic, environmental, and future energy security reasons. In this context, biofuels from lignocellulosic biomass and/or carbon-neutral fuels produced in the sustainable carbon cycle can close the carbon cycle and reach net zero-carbon emission. Recently, glycerol carbonate has been proposed as a promising fuel or fuel additive for future sustainability. Therefore, we investigated the hydrogen abstraction reactions of glycerol carbonate (GC) by OH radicals using high-level ab initio and variational transition state theory calculations. We mapped out the potential energy surface using the CCSD(T)/cc-pV(D, T)Z//MP2/cc-pVTZ level of theory. Here we used the ab initio parameters to obtain the site-specific rate coefficients by employing the variational transition state theory. We observed that every hydrogen atom in GC displays a unique reactivity with OH radicals. We derived branching ratio of each channel that are difficult to access experimentally. The overall rate coefficients exhibit a strong non-Arrhenius behaviour, which can be represented as: $k^{CVT/SCT}_{ov}$ (T) = 3.39 x 10 -20 x T 2.659 x e$\frac{-750.0 Jmol^{-1}}{RT}$ $\frac{cm^{3}}{molecule s}$ This is the first reported rate data for the glycerol carbonate and OH radicals reaction.

09 BIOMASS FUELS↗