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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A fast approximation to supershell partition functions

A formula for supershell partition functions, which play a major role in the Super Transition Array approach to radiative-opacity calculations, is derived as a functional of the distribution of energies within the supershell. It consists in an alternative expansion for an arbitrary number of electrons or holes which also allows for quick approximate evaluations with truncated number of terms in the expansion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Fast approximation to supershell partition functions: Explicit forms of the coefficients

In a previous work, we derived a formula for supershell partition functions, which are the cornerstone of the Super-Transition-Array approach to radiative-opacity calculations. The new expression takes the form of a functional of the distribution of energies within the supershell and allows for fast and accurate computations, truncating the number of terms in the expansion. The latter involves coefficients (denoted Γ $k$ ) for which we obtained a recursion relation. In the present short paper, as a complement of the previous one, we give an explicit formula for the coefficients Γ $k$ . Another recursion relation is also provided, as well as an alternative expression involving Bell polynomials. In conclusion, the connections with cycle indexes of permutation groups and with elementary symmetric polynomials are outlined.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

Stereotactic Radiosurgical Treatment of Brain Metastases to the Choroid Plexus;Renal cell cancer; Recursive partitioning analysis (RPA); Graded prognostic assessment (GPA); Survival and outcomes; Gamma knife

Purpose: Choroid plexus metastases (CPM) are uncommon lesions. Consequently, optimal management of CPM is uncertain. We summarize our experience with stereotactic radiosurgery (SRS) of CPM. Methods and Materials: Sixteen consecutive patients with presumed CPM treated with SRS between 1997 and 2007 were examined. Twelve were men with a median age at diagnosis of CPM of 61.9 {+-} 9.9 years; 14 had metastases from renal cell carcinoma (RCC). All patients had controlled primary disease at the time of treatment for CPM. Four patients with RCC and 1 with non-small-cell lung cancer had undergone whole-brain radiotherapy (WBRT) previously and 2 had received SRS to other brain metastases. The disease-free interval from the primary diagnosis to CPM diagnosis averaged 39.3 {+-} 46.2 months (range, 1.0-156.3). Five patients were asymptomatic; of the remaining 11, none had symptoms related to CPM. All presented with a single CPM. Results: Average maximum diameter of the CPMs was 2.0 {+-} 1.0 cm (range, 0.9-4.1 cm); mean volume was 2.4 {+-} 2.6 cm{sup 3} (range, 0.2-9.3). Median SRS dose was 24 Gy to the 53% isodose line (range, 14-24 Gy). Survival after SRS to the CPM was 25.3 {+-} 23.4 months (range, 3.2-101.6). Patients in Recursive Partitioning Analysis (RPA) class I (n = 10) had improved survival compared to those in class II (n = 6), as did those with better GPA scores. There were no local failures. After SRS, 1 patient underwent WBRT, 3 patients had one, and another had two subsequent SRS treatments to other brain lesions. Of the 14 patients who have died, 11 succumbed to systemic disease progression, 2 to progressive, multifocal central nervous system disease, and 1 to systemic disease with concurrent, stable central nervous system disease. There were no complications related to SRS. Conclusions: Most CPMs are associated with RCC. SRS represents a safe and viable treatment option as primary modality for these metastases, with excellent outcomes.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

New Breast Cancer Recursive Partitioning Analysis Prognostic Index in Patients With Newly Diagnosed Brain Metastases

Purpose: The aim of the study was to present a new breast cancer recursive partitioning analysis (RPA) prognostic index for patients with newly diagnosed brain metastases as a guide in clinical decision making. Methods and Materials: A prospectively collected group of 441 consecutive patients with breast cancer and brain metastases treated between the years 2003 and 2009 was assessed. Prognostic factors significant for univariate analysis were included into RPA. Results: Three prognostic classes of a new breast cancer RPA prognostic index were selected. The median survival of patients within prognostic Classes I, II, and III was 29, 9, and 2.4 months, respectively (p < 0.0001). Class I included patients with one or two brain metastases, without extracranial disease or with controlled extracranial disease, and with Karnofsky performance status (KPS) of 100. Class III included patients with multiple brain metastases with KPS of {<=}60. Class II included all other cases. Conclusions: The breast cancer RPA prognostic index is an easy and valuable tool for use in clinical practice. It can select patients who require aggressive treatment and those in whom whole-brain radiotherapy or symptomatic therapy is the most reasonable option. An individual approach is required for patients from prognostic Class II.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Recursive Partitioning Analysis Index Is Predictive for Overall Survival in Patients Undergoing Spine Stereotactic Body Radiation Therapy for Spinal Metastases

Purpose: To generate a prognostic index using recursive partitioning analysis (RPA) for patients undergoing spine stereotactic body radiation therapy (sSBRT) for spinal metastases (sMet). Methods and Materials: From an institutional review board-approved database, 174 patients were treated for sMet with sSBRT between February 2006 and August 2009. Median dose was 14 Gy (range, 8-24 Gy), typically in a single fraction (range, 1-5). Kaplan-Meier analysis was performed to detect any correlation between survival and histology. Histologies were divided into favorable (breast and prostate), radioresistant (renal cell, melanoma and sarcoma), and other (all other histologies). RPA was performed to identify any association of the following variables with overall survival (OS) following sSBRT: histology, gender, age, Karnofsky performance status (KPS), control of primary, extraosseous metastases, time from primary diagnosis (TPD), dose of sSBRT ({<=}14 Gy vs. >14 Gy), extent of spine disease (epidural only, bone and epidural, bone only), upfront or salvage treatment, presence of paraspinal extension, and previous surgery. Results: Median follow-up was 8.9 months. Median OS time from sSBRT was 10.7 months. Median OS intervals for favorable histologies were 14 months, 11.2 months for radioresistant histologies, and 7.3 months for other histologies (p = 0.02). RPA analysis resulted in three classes (p < 0.0001). Class 1 was defined as TPD of >30 months and KPS of >70; Class 2 was TPD of >30 months and KPS of {<=}70 or a TPD of {<=}30 months and age <70 years old; Class 3 was TPD of {<=}30 months and age {>=}70 years old. Median OS was 21.1 months for Class 1 (n = 59), 8.7 months for Class 2 (n = 104), and 2.4 months for Class 3 (n = 11). Conclusion: sSBRT patients treated for sMet have a wide variability in OS. We developed an RPA classification system that is predictive of OS. While many patients are treated for palliation of pain or to avoid symptomatic progression, this index may be used to predict which patients may benefit most from sSBRT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Subclassification of Recursive Partitioning Analysis Class II Patients With Brain Metastases Treated Radiosurgically

Purpose: Although the recursive partitioning analysis (RPA) class is generally used for predicting survival periods of patients with brain metastases (METs), the majority of such patients are Class II and clinical factors vary quite widely within this category. This prompted us to divide RPA Class II patients into three subclasses. Methods and Materials: This was a two-institution, institutional review board-approved, retrospective cohort study using two databases: the Mito series (2,000 consecutive patients, comprising 787 women and 1,213 men; mean age, 65 years [range, 19-96 years]) and the Chiba series (1,753 patients, comprising 673 female and 1,080 male patients; mean age, 65 years [range, 7-94 years]). Both patient series underwent Gamma Knife radiosurgery alone, without whole-brain radiotherapy, for brain METs during the same 10-year period, July 1998 through June 2008. The Cox proportional hazard model with a step-wise selection procedure was used for multivariate analysis. Results: In the Mito series, four factors were identified as favoring longer survival: Karnofsky Performance Status (90% to 100% vs. 70% to 80%), tumor numbers (solitary vs. multiple), primary tumor status (controlled vs. not controlled), and non-brain METs (no vs. yes). This new index is the sum of scores (0 and 1) of these four factors: RPA Class II-a, score of 0 or 1; RPA Class II-b, score of 2; and RPA Class II-c, score of 3 or 4. Next, using the Chiba series, we tested whether our index is valid for a different patient group. This new system showed highly statistically significant differences among subclasses in both the Mito series and the Chiba series (p < 0.001 for all subclasses). In addition, this new index was confirmed to be applicable to Class II patients with four major primary tumor sites, that is, lung, breast, alimentary tract, and urogenital organs. Conclusions: Our new grading system should be considered when designing future clinical trials involving brain MET patients.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Recursive Partitioning Analysis for New Classification of Patients With Esophageal Cancer Treated by Chemoradiotherapy

Background: The 7th edition of the American Joint Committee on Cancer staging system does not include lymph node size in the guidelines for staging patients with esophageal cancer. The objectives of this study were to determine the prognostic impact of the maximum metastatic lymph node diameter (ND) on survival and to develop and validate a new staging system for patients with esophageal squamous cell cancer who were treated with definitive chemoradiotherapy (CRT). Methods: Information on 402 patients with esophageal cancer undergoing CRT at two institutions was reviewed. Univariate and multivariate analyses of data from one institution were used to assess the impact of clinical factors on survival, and recursive partitioning analysis was performed to develop the new staging classification. To assess its clinical utility, the new classification was validated using data from the second institution. Results: By multivariate analysis, gender, T, N, and ND stages were independently and significantly associated with survival (p < 0.05). The resulting new staging classification was based on the T and ND. The four new stages led to good separation of survival curves in both the developmental and validation datasets (p < 0.05). Conclusions: Our results showed that lymph node size is a strong independent prognostic factor and that the new staging system, which incorporated lymph node size, provided good prognostic power, and discriminated effectively for patients with esophageal cancer undergoing CRT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism

In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothness and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Atom-partitioned multipole expansions for electrostatic potential boundary conditions

Applications such as grid-based real-space density functional theory (DFT) use the Poisson equation to compute electrostatics. However, the expected long tail of the electrostatic potential requires either the use of a large and costly outer domain or Dirichlet boundary conditions estimated via multipole expansion. We find that the oft-used single-center spherical multipole expansion is only appropriate for isotropic mesh domains such as spheres and cubes. In this work, we introduce a method suitable for high aspect ratio meshes whereby the charge density is partitioned into atomic domains and multipoles are computed for each domain. While this approach is moderately more expensive than a single-center expansion, it is numerically stable and still a small fraction of the overall cost of a DFT calculation. The net result is that when high aspect ratio systems are being studied, form-fitted meshes can now be used in lieu of cubic meshes to gain computational speedup.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

In-situ EBSD study of deformation behavior of retained austenite in a low-carbon quenching and partitioning steel via uniaxial tensile tests

Through using in-situ electron back-scattered diffraction and uniaxial tensile tests, this work mainly focuses on the deformation behavior of retained austenite (RA) in a low-carbon quenching and partitioning (Q&P) steel. In this paper, three different types of RA can be distinguished from different locations, respectively, RA grains at the triple edges, twinned austenite and RA grains positioned between martensite. The results have shown that grains at the triple edges and twinned austenite could transform easily with increasing strain, i.e. are less stable when compared with RA grains distributed between martensite that could resist a larger plastic deformation. Meanwhile, the strain leads to rotations of RA grains distributed at the triple edges and between martensite. Moreover, RA grains with a similar orientation undergone similar rotations with the same true strain. These RA grains rotated along a specific slip plane and slip direction and the grain rotation is taken as a significant factor to improve the ductility of steel. In addition, grain sizes of RA decreased gradually with an increase of true strain and smaller (0–0.2 μm) grains were more capable of resisting the deformation. According to kernel average misorientation (KAM) analysis, it can be found that strain distribution is preferentially localized near martensite–austenite phase boundaries and in the interior of martensite. The average KAM values increased continuously with increasing true strain. - Highlights: •The in-situ and ex-situ tensile specimens differ to some extent in mechanical properties. •Retained austenite grains at the triple edges and twinned austenite transformed easily at the early stage of true strain. •Film-like retained austenite grains only rotated prior to the transformation during straining. •Retained austenite grains having with a similar orientation experienced similar rotations during the same true strain.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Effect of iodides on thermal behavior and phase partitioning in LiCl-KCl

Liquid-fueled molten salt reactors (MSRs) are designed to operate with fissile materials and, ultimately, fission products dissolved in the primary molten salt coolant. Understanding the speciation and transport of iodine—a high-yield fission product—is essential because this element’s accidental release poses significant environmental concerns due to its capacity to be readily absorbed by the human thyroid gland. Here, we report the impact of iodide species (LiI and KI) on phase transitions, phase distribution, and phase stability in LiCl–KCl-eutectic salt mixtures. The study employed a combination of computational and experimental techniques, including thermodynamic FactSage calculations, differential scanning calorimetry, and high-temperature X-ray diffraction. The results indicate that the presence of iodide (10–25 wt%) significantly alters the melting behavior of the LiCl–KCleutectic system. Adding 10 wt% LiI has a more-pronounced effect than 10 wt% KI, as LiI converts to KI, leading to formation of LiCl, thereby, altering the LiCl-KCl ratio which significantly affects the melting temperature of the mixture. Furthermore, the evolution of crystalline structure, solid-fraction composition, and the dynamics of mixed-halide solid–liquid partitioning as a function of temperature indicate the potential for selective iodide separation from chloride-salt mixtures via solid–liquid separation techniques. Overall, the presented findings provide valuable insights that are beneficial for the design and operation of MSRs, as well as for the safe handling and effective processing of used nuclear fuel using advanced pyrochemical techniques.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Helium partitioning to the core-shelled Ta nanoclusters in nanocrystalline Cu-Ta alloy

In this work, a nanocrystalline (NC) Cu-10at.%Ta alloy is irradiated with helium at different temperatures to assess the stability and effectiveness of Ta nanoclusters in trapping helium and suppressing swelling. Advanced microstructural characterization of the room-temperature irradiated specimens indicated the presence of small He-bubbles (∼1-2 nm) at the peak damage depth mainly at the core and along the interface of Ta nanoclusters with Cu matrix. Few bubbles were found along grain boundaries, with much smaller bubbles homogenously distributed within the copper lattice. High-temperature irradiation exhibited bubbles of ∼3-5 nm, which were primarily associated with nanoclusters as compared to other locations, with no observed faceting of the bubbles. In conclusion, atom probe analysis confirmed helium partitioning to the Ta nanoclusters indicating the effective entrapment of these He atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2011

A comparison of trenched plot techniques for partitioning soil respiration

Partitioning the soil surface CO{sub 2} flux (R{sub S}) flux is an important step in understanding ecosystem-level carbon cycling, given that R{sub S} is poorly constrained and its source components may have different responses to climate change. Trenched plots are a classic method of separating the R{sub S} source fluxes, but labor-intensive and may cause considerable disturbance to the soil environment. This study tested if various methods of plant suppression in trenched plots affected R{sub S} fluxes, quantified the R{sub S} response to soil temperature and moisture changes, and estimated the heterotrophic contribution to R{sub S}. It was performed in a boreal black spruce (Picea mariana) plantation, using a complete randomized design, during the 2007 growing season (May-November). Trenched plots had significantly lower R{sub S} than control plots, with differences appearing {approx}100 days after trenching; spatial variability doubled after trenching but then declined throughout the experiment. Most trenching treatments had significantly lower (by {approx}0.5 {mu}mol m{sup -2} s{sup -1}) R{sub S} than the controls, and there was no significant difference in R{sub S} among the various trenching treatments. Soil temperature at 2 cm explained more R{sub S} variability than did 10-cm temperature or soil moisture. Temperature sensitivity (Q10) declined in the control plots from {approx}2.6 (at 5 C) to {approx}1.6 (at 15 C); trenched plots values were higher, from 3.1 at 5 C to 1.9 at 15 C. We estimated R{sub S} for the study period to be 241 {+-} 40 g C m{sup -2}, with roots contributing 64% of R{sub S} after accounting for fine root decay, and 293 g C m{sup -2} for the entire year. These findings suggest that laborious hand weeding of vegetation may be usefully replaced by other methods, easing future studies of this large and poorly-understood carbon flux.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2012

Thermodynamic analysis on heavy metals partitioning impacted by moisture during the MSW incineration

Highlights: Black-Right-Pointing-Pointer Partitioning of HMs affected by moisture was investigated by thermodynamic analysis. Black-Right-Pointing-Pointer Increase in moisture and in temperature was opposite impact on HMs contribution. Black-Right-Pointing-Pointer The extent of temperature decreased by increase in moisture determines the impact. - Abstract: A thermodynamic calculation was carried out to predict the behavior and speciation of heavy metals (HMs), Pb, Zn, Cu, and Cd, during municipal solid waste (MSW) incineration with the different moisture levels. The calculation was based on the minimization of the total Gibbs free energy of the multi-components and multi-phases closed system reaching chemical equilibrium. The calculation also indicated the reaction directions and tendencies of HMs components. The impacts of chlorine additives (No PVC, 1%PVC, and 5%PVC) and moisture on the behavior of HMs were investigated at different temperature levels in the system (750 Degree-Sign C, 950 Degree-Sign C, and 1150 Degree-Sign C). Furthermore, because the incineration temperature falls down with the increase in moisture in waste, the co-influence of moisture and temperature in combusting MSW on the HMs was also studied with the given chlorine (as 1%PVC + 0.5%NaCl). The results showed that in the non-chlorine system, the impact of the moisture on Pb, Zn, and Cu was not significant, and the ratio of compound transformation was less than 10%, except the Cd compounds at 950 Degree-Sign C and 1150 Degree-Sign C. In the system with low chlorine (as 1%PVC) at constant temperature, the chlorides of HMs (Cd, Pb, Zn, and Cu) transferred to oxides, and when the content of chlorine rose up (as 5%PVC), the ratio of the chlorides of HMs (Cd, Pb, Zn, and Cu) transferring to oxides fell down noticeably. When the moisture varied together with the temperature, the Zn and Cu compounds transferred from chlorides to oxides with increase in moisture as well as decrease in temperature. At the temperature of 700-1000 Degree-Sign C, the impact of temperature on Pb and Cd was little and the moisture was the main factor; while at the temperature of 1000-1200 Degree-Sign C, the impact of increase in moisture and decrease in temperature on Pb and Cd was almost equal and reversed.

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

Periodic GFN1-xTB Tight Binding: A Generalized Ewald Partitioning Scheme for the Klopman–Ohno Function

A novel formulation is presented for the treatment of electrostatics in the periodic GFN1-xTB tight-binding model. Periodic GFN1-xTB is hindered by the functional form of the second-order electrostatics, which only recovers Coulombic behavior at large interatomic distances and lacks a closed-form solution for its Fourier transform. We address this by introducing a binomial expansion of the Klopman–Ohno function to partition short- and long-range interactions, enabling the use of a generalized Ewald summation for the solution of the electrostatic energy. This approach is general and is applicable to any damped potential of the form |R n + c| –m . Benchmarks on the X23 molecular crystal dataset and a range of prototypical bulk semiconductors demonstrate that this systematic treatment of the electrostatics eliminates unphysical behavior in the equation of state curves. In the bulk systems studied, we observe a mean absolute error in total energy of 35 meV/atom, comparable to the machine-learned universal force field, M3GNet, and sufficiently precise for structure relaxation. These results highlight the promising potential of GFN1-xTB as a universal tight-binding parametrization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2018

Anharmonic Rovibrational Partition Functions for Fluxional Species at High Temperatures via Monte Carlo Phase Space Integrals

Monte Carlo phase space integration (MCPSI) is used to compute full dimensional and fully anharmonic, but classical, rovibrational partition functions for 22 small- and medium-sized molecules and radicals. Several of the species considered here feature multiple minima and low-frequency nonlocal motions, and efficiently sampling these systems is facilitated using curvilinear (stretch, bend, and torsion) coordinates. The curvilinear coordinate MCPSI method is demonstrated to be applicable to the treatment of fluxional species with complex rovibrational structures and as many as 21 fully coupled rovibrational degrees of freedom. Trends in the computed anharmonicity corrections are discussed. For many systems, rovibrational anharmonicities at elevated temperatures are shown to vary consistently with the number of degrees of freedom and with temperature once rovibrational coupling and torsional anharmonicity are accounted for. In conclusion, larger corrections are found for systems with complex vibrational structures, such as systems with multiple large-amplitude modes and/or multiple minima.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Anharmonic Rovibrational Partition Functions at High Temperatures: Tests of Reduced-Dimensional Models for Systems with up to Three Fluxional Modes

In this work, curvilinear coordinate Monte Carlo phase space integration and a series of full-dimensional fitted potential energy surfaces are used to study the effectiveness of reduced-dimensional models for predicting rovibrational anharmonicity at high temperatures. Fully coupled and fully anharmonic, but classical, rovibrational partition functions Q are computed for 14 species with two or three fluxional modes (inversions or torsions) and as many as 30 degrees of freedom. These results are converted to semiclassical anharmonicity correction factors f and are analyzed alongside results obtained previously for 22 species with up to two fluxional modes. As expected, fluxional species show considerable variation in f at high temperatures; f is as small as 0.2 for acetone and is as large as 9 for methylene glycol at 2500 K. This set of full-dimensional results is used to test the accuracy of reduced-dimensional models where fluxional modes are treated as coupled to one another but as separable from the remaining nonfluxional modes. For most systems, we find that such an approximation is accurate at high temperatures, with average errors in Q of just similar to 25%. For some systems, however, larger errors are found, and these are attributed to strong coupling of the fluxional modes to one or more nonfluxional modes. In particular, we identify strong coupling to low-frequency bends for some systems, and we show that by comparing curvilinear and rectilinear harmonic frequencies for the fluxional modes, we can estimate the effect of this coupling on rovibrational anharmonicity. We also quantify the accuracy of the more severe but common assumption of treating fluxional modes as separable from one another, that is, as sets of uncoupled one-dimensional inversions and torsions. This approach can work well for methyl and alkyl rotors, but it is shown to have errors as large as a factor of 7 at high temperatures for more complex systems. Lastly, we note that while the present analysis focuses on the treatment of fluxional modes, the collective anharmonicity correction associated with the more numerous nonfluxional modes, although simpler to describe, comprises a significant fraction of the overall anharmonicity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗