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At least 217 records · Page 12

Neural Network Solver for Small Quantum Clusters

Machine learning approaches have recently been applied to the study of various problems in physics. Most of these studies are focused on interpreting the data generated by conventional numerical methods or the data on an existing experimental database. An interesting question is whether it is possible to use a machine learning approach, in particular a neural network, for solving the many-body problem. In this paper, we present a neural network solver for the single impurity Anderson model, the paradigm of an interacting quantum problem in small clusters. We demonstrate that the neural-network-based solver provides quantitative accurate results for the spectral function as compared to the exact diagonalization method. This opens the possibility of utilizing the neural network approach as an impurity solver for other many-body numerical approaches, such as the dynamical mean field theory.

36 MATERIALS SCIENCE↗

Model for the Solid–Liquid Interfacial Free Energy at High Pressures

The free energy involved in the formation of an interface between two phases (e.g., a solid–liquid interface) is referred to as the interfacial free energy. For the case of solidification, the interfacial free energy dictates the height of the energy barrier required to nucleate stable clusters of the newly forming solid phase and is essential for producing an accurate solidification kinetics model using classical nucleation theory (CNT)-based methods. While various methods have been proposed for modeling the interfacial free energy for solid–liquid interfaces in prior literature, many of these formulations involve making restrictive assumptions or approximations, such as the system being at or near equilibrium (i.e., the system temperature is approximately equal to the melt temperature) or that the system is at pressures close to atmospheric. However, these approximations and assumptions may break down in highly non-equilibrium situations, such as in dynamic-compression experiments where metastable liquids that are undercooled by hundreds of kelvin or over-pressurized by several gigapascals or more are formed before eventually solidifying. We derive a solid–liquid interfacial free-energy model for such high-pressure conditions by considering the enthalpies of interactions between pairs of atoms or molecules. We also consider the contribution of interface roughness (disordering) by incorporating a multilayer interface model known as the Temkin n-layer model. Our formulation is applicable to a diverse variety of materials, and we demonstrate it by developing models specifically for two different materials: water and gallium. We apply our interfacial free-energy formulation to CNT-based kinetics simulations of several suites of dynamic-compression experiments that cause liquid water to solidify to the high-pressure solid polymorph ice VII and have found good agreement to the observed kinetics with only minor empirical fitting.

36 MATERIALS SCIENCE↗

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Buchert, T.↗

High spatiotemporal variability of bacterial diversity over short time scales with unique hydrochemical associations within a shallow aquifer

Understanding microbial community structure and function within the subsurface is critical to assessing overall quality and maintenance of groundwater; however, the factors that determine microbial community assembly, structure, and function in groundwater systems and their impact on water quality remains poorly understood. In this study, three shallow wells (FW301, FW303, FW305) in a non-contaminated shallow aquifer in the ENIGMA-Oak Ridge Field Research Center (Oak Ridge, TN) were sampled approximately 3 times a week over a period of three months to measure changes in groundwater geochemistry and microbial diversity. It was expected that the sampled microbial diversity from two historic field wells (FW301, FW303) would be relatively stable, while diversity from a newer well (FW305) would be less stable over time. The wells displayed some degree of hydrochemical variability over time unique to each well, with FW303 being overall the most stable well and FW301 being the most dynamic based upon dissolved oxygen, conductivity, and nitrate. Community analysis via ss-rRNA paired-end sequencing and distribution-based clustering revealed higher OTU richness, diversity, and variability in groundwater communities of FW301 than the other two wells for diversity binned over all time points. Microbial community composition of a given well was on average > 50% dissimilar to any other well at a given time (days), yet, functional gene diversity as measured with GeoChip remained relatively constant. Similarities in community structure across wells were observed with respect to the presence of 20 shared bacterial groups in all samples in all wells, although at varying levels over the tested time period. Similarity percentage (SIMPER) analysis revealed that variability in FW301 was largely attributed to low abundance, highly-transient populations, while variability in the most hydrochemically stable well (FW303) was due to fluctuations in more highly abundant and frequently present taxa. Additionally, the youngest well FW305 showed a dramatic shift in community composition towards the end of the sampling period that was not observed in the other wells, suggesting possible succession events over time. Time-series analysis using vector auto-regressive models and Granger causality showed unique relationships between richness and geochemistry over time in each well. Finally, these results indicate temporally dynamic microbial communities over short time scales, with day-to-day population shifts in local community structure influenced by available source community diversity and local groundwater hydrochemistry.

59 BASIC BIOLOGICAL SCIENCES↗

Status on the Development of a Modeling and Simulation Framework for the Economic Assessment of Nuclear Hybrid Energy Systems

An effort to design and build a modeling and simulation framework to assess the economic viability of Nuclear Hybrid Energy Systems (NHES) was undertaken in fiscal year 2015 (FY15). The purpose of this report is to document the various tasks associated with the development of such a framework and to provide a status on its progress. Several tasks have been accomplished. First, starting from a simulation strategy, a rigorous mathematical formulation has been achieved in which the economic optimization of a Nuclear Hybrid Energy System is presented as a constrained robust (under uncertainty) optimization problem. Some possible algorithms for the solution of the optimization problem are presented. A variation of the Simultaneous Perturbation Stochastic Approximation algorithm has been implemented in RAVEN and preliminary tests have been performed. The development of the software infrastructure to support the simulation of the whole NHES has also moved forward. The coupling between RAVEN and an implementation of the Modelica language (OpenModelica) has been implemented, migrated under several operating systems and tested using an adapted model of a desalination plant. In particular, this exercise was focused on testing the coupling of the different code systems; testing parallel, computationally expensive simulations on the INL cluster; and providing a proof of concept for the possibility of using surrogate models to represent the different NHES subsystems. Another important step was the porting of the RAVEN code under the Windows™ operating system. This accomplishment makes RAVEN compatible with the development environment that is being used for dynamic simulation of NHES components. A very simplified model of a NHES on the electric market has been built in RAVEN to confirm expectations on the analysis capability of RAVEN to provide insight into system economics and to test the capability of RAVEN to identify limit surfaces even for stochastic constraints. This capability will be needed in the future to enforce the stochastic constraints on the electric demand coverage from the NHES. The development team gained experience with many of the tools that are currently envisioned for use in the economic analysis of NHES and completed several important steps. Given the complexity of the project, preference has been given to a structural approach in which several independent efforts have been used to build the cornerstone of the simulation framework. While this is good approach in establishing such a complex framework, it may delay reaching more complete results on the performance of analyzed system configurations. The integration of the previously reported exergy analysis approach was initially proposed as part of this milestone. However, in reality, the exergy-based apportioning of cost will take place only in a second stage of the implementation since it will be used to properly allocate cost among the different NHES subsystems. Therefore, exergy does not appear at the level of the main drivers in the analysis framework; the latter development of the base framework is the focus of this report.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

U.S. stock market interaction network as learned by the Boltzmann machine

Here, we study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters inferred using exact and approximate learning algorithms. Since the model and inference methods require use of binary variables, effect of this mapping of continuous returns to the discrete domain is studied. The presented results show that binarization preserves the correlation structure of the market. Properties of distributions of external fields and couplings as well as the market interaction network and industry sector clustering structure are studied for different historical dates and moving window sizes. We demonstrate that the observed positive heavy tail in distribution of couplings is related to the sparse clustering structure of the market. We also show that discrepancies between the model’s parameters might be used as a precursor of financial instabilities.

97 MATHEMATICS AND COMPUTING↗

Full-Dimensional Quantum Dynamics of SiO in Collision with H 2

Here, we report the first full-dimensional potential energy surface (PES) and quantum mechanical close-coupling calculations for scattering of SiO due to H 2 . The full-dimensional interaction potential surface was computed using the explicitly correlated coupled-cluster (CCSD(T)-F12b) approach and fitted using an invariant polynomial approach. Pure rotational quenching cross sections from initial states v 1 = 0, j 1 = 1–5 of SiO in collision with H 2 are calculated for collision energies between 1.0 and 5000 cm –1 . State-to-state rotational rate coefficients are calculated at temperatures between 5 and 1000 K. The rotational rate coefficients of SiO with para-H 2 (p-H 2 ) are compared with previous approximate findings which were obtained using SiO-He PESs or scaled from SiO-He rate coefficients. Rovibrational state-to-state and total quenching cross sections and rate coefficients for initially excited SiO (v 1 = 1, j 1 = 0 and 1) in collisions with p-H 2 (v 2 = 0, j 2 = 0) and ortho-H 2 (o-H 2 ) (v 2 = 0, j 2 = 1) are also obtained. The application of the current collisional rate coefficients to astrophysics is briefly discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Photoelectron spectra of copper oxide cluster anions from first principles methods

We present results and analyses for the photoelectron spectra of small copper oxide cluster anions (CuO – , CuO – 2 , CuO – 3 , and Cu 2 O – ). The spectra are computed using various techniques, including density functional theory (DFT) with semi-local, global hybrid, and optimally tuned range-separated hybrid functionals, as well as many-body perturbation theory within the GW approximation based on various DFT starting points. The results are compared with each other and with the available experimental data. We conclude that as in many metal-organic systems, self-interaction errors are a major issue that is mitigated by hybrid functionals. However, these need to be balanced against a strong role of non-dynamical correlation—especially in smaller, more symmetric systems—where errors are alleviated by semi-local functionals. In conclusion, the relative importance of the two phenomena, including practical ways of balancing the two constraints, is discussed in detail.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Solar Wind Excitation of Pc5 Fluctuations in the Magnetosphere and on the Ground

The primary purpose of this paper is to show the strong link between solar wind compressional fluctuations in the 1-8 mHz frequency range and Pc5 fluctuations in the magnetosphere near the magnetopause, at geosynchronous orbit, over the poles, and on the ground. We focus on a time interval in March and April 2002 when there was a favorable alignment of satellites combined with ten high speed solar wind streams. We used the S3C Great Observatory: specifically, ACE and Wind in the solar wind, Geotail near the magnetopause, GOES 8 and 10 at geosynchronous orbit, Cluster over the poles, and CANOPUS/CARISMA ground stations near the footpoints of magnetic field lines connected to either the magnetopause or the GOES satellites. Using four examples and a statistical survey we show that magnetospheric Pc5 fluctuations exist regardless of IMF orientation and for a wide range of speeds and dynamic pressures; the amplitude and power of magnetospheric fluctuations depends primarily on the amplitude and power of solar wind dynamic pressure fluctuations. The driving and response frequency of these geoeffective fluctuations is in the range 0.5 - 4 mHz. The most striking magnetospheric response occurs when the solar wind speed, dynamic pressure, and dynamic pressure fluctuations all increase at approximately the same time, as frequently occurs near the leading edge of high speed streams. We show evidence of oscillating Poynting Flux at the magnetopause determined using Geotail data that both excites a FLR and propagates evanescently inward. These observations suggest that, at least for this time interval at spring equinox, the entry path is from the dayside equatorial magnetopause inward; multiple field line resonances may be excited from the magnetopause to geosynchronous orbit by propagating compressional waves, with the power decreasing inward away from the magnetopause.

Kessel, Ramona L.↗

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: N-body mock challenge for the eBOSS emission line galaxy sample

ABSTRACT Cosmological growth can be measured in the redshift space clustering of galaxies targeted by spectroscopic surveys. Accurate prediction of clustering of galaxies will require understanding galaxy physics, which is a very hard and highly non-linear problem. Approximate models of redshift space distortion (RSD) take a perturbative approach to solve the evolution of dark matter and galaxies in the universe. In this paper, we focus on extended Baryon Oscillation Spectroscopic (eBOSS) emission line galaxies (ELGs) that live in intermediate mass haloes. We create a series of mock catalogues using haloes from the Multidark and outer rim dark matter only N-body simulations. Our mock catalogues include various effects inspired by baryonic physics such as assembly bias and the characteristics of satellite galaxies kinematics, dynamics, and statistics deviating from dark matter particles. We analyse these mocks using the TNS RSD model in Fourier space and the convolution Lagrangian perturbation theory (CLPT) in configuration space. We conclude that these two RSD models provide an unbiased measurement of RSD within the statistical error of our mocks. We obtain the conservative theoretical systematic uncertainty of $3.3{{\ \rm per\ cent}}$, $1.8{{\ \rm per\ cent}}$, and $1.5{{\ \rm per\ cent}}$ in fσ8, α∥, and α⊥, respectively, for the TNS and CLPT models. We note that the estimated theoretical systematic error is an order of magnitude smaller than the statistical error of the eBOSS ELG sample and hence are negligible for the purpose of the current eBOSS ELG analysis.

Alam, Shadab↗

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe–2S] Systems: A Benchmark Study of the [Fe 2 S 2 (SCH 3 ) 4 ] 2–,3–,4– , [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S- p -tol) 4 ] 2– , and [Fe 2 S 2 (S- o -xyl) 4 ] 2– Complexes

Iron–sulfur clusters are crucial for biological electron transport and catalysis. Obtaining accurate geometries, energetics, manifolds of their excited electronic states, and reduction energies is important to understand their role in these processes. Here, using a [2Fe–2S] model complex with Fe II and Fe III oxidation states, which leads to different charges, i.e., [Fe 2 S 2 (SMe) 4 ] 2–,3–,4– , we benchmarked a variety of computational methodologies ranging from density functional theory (DFT) to post-Hartree–Fock methods, including complete active space self-consistent field (CASSCF), multireference configuration interaction, the second-order N-electron valence state perturbation theory (NEVPT2), and the linearized integrand approximation of adiabatic connection (AC0) approaches. Additionally, we studied three experimentally well-characterized complexes, [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S-o-tol) 4 ] 2– , and [Fe 2 S 2 (S-o-xyl) 4 ] 2– , via DFT methods. We conclude that the dynamic electron correlation is important for accurately predicting the geometry of these complexes. Broken symmetry (BS) DFT correctly predicts experimental geometries of low-spin multiplicity, while CASSCF does not. However, BS-DFT significantly overestimates the difference between the low- and high-spin electronic states for a given oxidation state. At the same time, CASSCF underestimates it but provides relative energies closer to the reference NEVPT2 results. Finally, AC0 provides energetics of NEVPT2 quality with the additional advantage of being able to use large CASSCF sizes. NEVPT2 gives the best estimates of the Fe III /Fe III → Fe II /Fe III (4.27 eV) and Fe II /F III → Fe II /F II (7.72 eV) reduction energies. The results provide insight into the electronic structure of these complexes and assist in the understanding of their physical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigation into the transport properties of planetary interiors through inelastic X-ray scattering experiments and quantum molecular dynamics (Final Technical Report)

This was a two-year research project for the period 08/15/2018 - 08/14/2020 conducted at the University of Nevada, Reno using Pronghorn, a newly built high-performance cluster located at the University. The short-term project goal was to provide computational support for the experimental campaigns at LCLS through data analysis of previous and upcoming scheduled experiments, along with performing state-of-the-art atomistic simulations of dense plasmas. The longer-term goal was to create a new computational high energy density physics group located at the University of Nevada, Reno. Guided by results from past and future high-resolution scattering experiments, we aimed to research and develop non-equilibrium and non-adiabatic atomistic simulations of dense plasmas that went beyond the Born-Oppenheimer approximation

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Scalable, In-situ Data Clustering Data Analysis for Extreme Scale Scientific Computing (Final Report)

The objective of this project is to address challenges in the design and development of scalable in-situ data clustering and analytics algorithms and software. Our goal is to develop parallel software consisting of a set of spatio-temporal data clustering and anomaly detection functions, both of which are very important for large-scale analysis and have wide applicability for in-situ runs as well as post-processing analysis. Our design principles for in-situ analysis consider the following: (1) identify parts of the computation can be done close to the data within the nodes, while it is still in memory; (2) extract analysis components can (and should) be performed in remote staging and analysis nodes; (3) develop error-bound approximation methods for applications tolerable for small errors; (4) identify the type of derived distributions and statistics, for spatio-temporal data, that can be kept locally in order to both accelerate computations and meet energy constraints in subsequent iterations and phases; (5) use a self-describing data format so that data can be consistent and understood among local storage (memory and SSDs) and at staging and analysis nodes, thereby providing portability and flexibility; (6) develop service-oriented functions that can schedule in-situ and post-hoc analysis tasks based on the dynamic requirements of applications. Our development focus is to produce the parallel data analysis software/library that will be scalable, reusable, extensible, and generic for applications in different disciplines. The software will be able to run in-situ with the simulations as well as post-hoc analysis. This approach will satisfy many synergistic requirements for data intensive applications executed on data coming from instruments and experiments. In particular, the proposed multilevel approach is directly applicable to perform design tradeoffs for running part of the algorithms near the instruments and the rest on remote (analysis) systems.

97 MATHEMATICS AND COMPUTING↗

Flood Inundation Mapping in the Logone Floodplain from Multi Temporal Landsat ETM+Imagery

Yearly flooding in the Logone floodplain makes an impact on agricultural, pastoral, and fishery systems in the Lake Chad Basin. Since the flooding extent and depth are highly variable, flood inundation mapping helps us make better use of water resources and prevent flood hazards in the Logone floodplain. The flood maps are generated from 33 multi temporal Landsat Enhanced Thematic Mapper Plus (ETM+) during three years 2006 to 2008. Flooded area is classified using a short-wave infrared band whereas open water is classified by Iterative Self-organizing Data Analysis (ISODATA) clustering. The maximum flooding extent in the study area increases up to approximately 5.8K km2 in late October 2008. The study also provides strong correlation of the flooding extents with water height variations in both the floodplain and the river based on a second polynomial regression model. The water heights are from ENIVSAT altimetry in the floodplain and gauge measurements in the river. Coefficients of determination between flooding extents and water height variations are greater than 0.91 with 4 to 36 days in phase lag. Floodwater drains back to the river and to the northeast during the recession period in December and January. The study supports understanding of the Logone floodplain dynamics in detail of spatial pattern and size of the flooding extent and assists the flood monitoring and prediction systems in the catchment.

Jung, Hahn Chul↗

Mildly Hierarchical Triple Dynamics and Applications to the Outer Solar System

Three-body interactions are ubiquitous in astrophysics. For instance, Kozai–Lidov oscillations in hierarchical triple systems have been studied extensively and applied to a wide range of astrophysical systems. However, mildly hierarchical triples also play an important role, but they are less explored. In this work, we consider the secular dynamics of a test particle in a mildly hierarchical configuration. We find the limit within which the secular approximation is reliable when the outer perturber is in a circular orbit. In addition, we present resonances and chaotic regions using surface-of-section plots, and characterize regions of phase space that allow large eccentricity and inclination variations. Finally, we apply the secular results to the outer Solar System. We focus on the distribution of extreme trans-Neptunian objects (eTNOs) under the perturbation of a possible outer planet (Planet 9), and find that in addition to a low-inclination Planet 9, a polar or a counter-orbiting one could also produce pericenter clustering of eTNOs, while the polar one leads to a wider spread of eTNO inclinations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exact closed-form unitary transformations of fermionic operators

Unitary transformations play a fundamental role in many-body physics, and except for special cases, they are not expressible in closed form. We present closed-form expressions for unitary transformations generated by a single fermionic operator for Hermitian and anti-Hermitian generators. We demonstrate the usefulness of these expressions in formal analyses of unitary transformations and numerical applications to Hamiltonian downfolding in quantum computing and Heisenberg dynamics. Furthermore, this work paves the way for new analytical treatments of unitary transformations and numerical many-body methods for fermions.

74 ATOMIC AND MOLECULAR PHYSICS↗

The Singlet–Triplet Gap of Cyclobutadiene: The CIPSI-Driven CC( P ; Q ) Study

An accurate determination of singlet−triplet gaps in biradicals, including cyclobutadiene in the automerization barrier region where one has to balance the substantial nondynamical many-electron correlation effects characterizing the singlet ground state with the predominantly dynamical correlations of the lowest-energy triplet, remains a challenge for many quantum chemistry methods. High-level coupled-cluster (CC) approaches, such as the CC method with a full treatment of singly, doubly, and triply excited clusters (CCSDT), are often capable of providing reliable results, but routine application of such methods is hindered by their high computational costs. We have recently proposed a practical alternative to converging the CCSDT energetics at small fractions of the computational effort, even when electron correlations become stronger and connected triply excited clusters are larger and nonperturbative, by merging the CC(P;Q) moment expansions with the selected configuration interaction methodology abbreviated as CIPSI. We demonstrate that one can accurately approximate the highly accurate CCSDT potential surfaces characterizing the lowest singlet and triplet states of cyclobutadiene along the automerization coordinate and the gap between them using tiny fractions of triply excited cluster amplitudes identified with the help of relatively inexpensive CIPSI Hamiltonian diagonalizations.

Basis sets↗

Characterization of the 2-methylvinoxy radical + O 2 reaction: A focal point analysis and composite multireference study

Vinoxy radicals are involved in numerous atmospheric and combustion mechanisms. High-level theoretical methods have recently shed new light on the reaction of the unsubstituted vinoxy radical with O 2 . The reactions of 1-methylvinoxy radical and 2-methylvinoxy radical with molecular oxygen have experimental high pressure limiting rate constants, k ∞ , 5–7 times higher than that of the vinoxy plus O 2 reaction. In this work, high-level ab initio quantum chemical computations are applied to the 2-methylvinoxy radical plus O 2 system, namely, the formation and isomerization of the 1-oxo-2-propylperoxy radical, the immediate product of O 2 addition to the 2-methylvinoxy radical. Multireference methods were applied to the entrance channel. No barrier to O 2 addition could be located, and more sophisticated treatment of dynamic electron correlation shows that the principal difference between O 2 addition to the vinoxy and 2-methylvinoxy radicals is a larger steric factor for 2-methylvinoxy + O 2 . This is attributed to the favorable interaction between the incoming O 2 molecule and the methyl group of the 2-methylvinoxy radical. Via the focal point approach, energetics for this reaction were determined, in most cases, to chemical accuracy. The coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] correlation energy and Hartree–Fock energies were independently extrapolated to the complete basis set limit. A correction for the effect of higher excitations was computed at the CCSDT(Q)/6-31G level. Corrections for the frozen-core approximation, the Born–Oppenheimer approximation, the nonrelativistic approximation, and the zero-point vibrational energy were included. From the 1-oxo-2-propylperoxy radical, dissociation to reactants is competitive with the lowest energy isomerization pathway. The lowest energy isomerization pathway ultimately forms acetaldehyde, CO, and ·OH as the final products.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗