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

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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Tailoring Cu-Zr gradient nanoglass structures: Influence of nanoparticle size and cooling rates on glass-glass interfaces

The study of gradient nanoglasses (GNGs) has gained attention due to their unique mechanical properties and potential applications in advanced materials. This study employs molecular dynamics simulations to synthesize a GNG using Cu-Zr metallic glass nanoparticles (NPs) sized from 3 to 15 nm. The NPs were produced by melting and quenching metallic clusters at a relatively slow quench rate of 10 9 K/s. The synthesis of GNG is elucidated along with the characterization of its heterogeneous metallic glass nanostructure. A seamless GNG structure is formed through cold compression of Cu 64 Zr 36 amorphous NPs of varying sizes. The influence of NP size on the GNG structure is investigated, utilizing deeply relaxed NPs, which exhibit a characteristic Cu segregation pattern on their surfaces. The results highlight an increase in structural heterogeneity due to heterogeneous mass transport and the development of local composition and density variations caused by Cu segregation at glass-glass interfaces (GGIs). A reduction in NP size is correlated with decreased Cu atomic displacements and local density at GGIs, suggesting that larger NPs may produce stronger GGIs. This research presents a novel methodology for synthesizing heterogeneous metallic glasses, demonstrating the capacity to control and customize nanostructure heterogeneity through the manipulation of NP sizes and cooling rates. Furthermore, these findings enhance our understanding of structural evolution during nanoglass synthesis and lay the foundation for further exploration in nanomaterial synthesis and characterization.

36 MATERIALS SCIENCE↗
NASA NTRS1994

Anatomy of a Photodissociation Region: High angular resolution images of molecular emission in the Orion Bar

We present observations of the molecular component of the Orion Bar, a prototypical Photodissociation Region (PDR) illuminated by the Trapezium cluster. The high angular resolution (6 sec-10 sec) that we have achieved by combining single-dish and interferometric observations has allowed us to examine in detail the spatial and kinematic morphology of this region and to estimate the physical characteristics of the molecular gas it contains. Our observations indicate that this PDR can be essentially described as a homogeneously distributed slab of moderately dense material (approximately 5 x 10(exp 4)/cu cm), in which are embedded a small number of dense (greater than 10(exp 6)/cu cm) clumps. The latter play little or no role in determining the thickness and kinetic temperature structure of this PDR. This observational picture is largely supported by PDR model calculations for this region, which we describe in detail in this work. We also find our model predictions of the intensities of a variety of atomic and molecular lines to be in good general agreement with a number of previous observations.

Tauber, Jan A.↗
DOE OSTI2023

Molecular dynamics study of primary damage in the near-surface region in nickel

In this work, we carried out a large-scale molecular dynamics (MD) simulation to elucidate the effect of the free surface on the defect production of displacement cascades in pure nickel. These MD simulations were performed both in the bulk and near-surface regions with primary knock-on atom (PKA) energies of E PKA = 1, 5, or 10 keV and at temperatures T = 300, 425, or 525 K. Additionally, for every (T, E PKA ), near-surface cascade simulations were performed as a function of depth. In the near-surface simulations, assuming isotropic neutron fluence, the PKAs were initiated in random directions, including toward and parallel to the free surface. For both the near-surface and bulk cascades, the effect of E PKA and T on the defect production is similar. In both cases, the defect production increases with E PKA , but the temperature has minimal effect. However, the production and clustering of vacancies are higher for near-surface cascades, and they decrease with increasing depth. In contrast, the production and clustering of self-interstitial atoms are lower and increase with depth. Eventually, the production and clustering of both defect types approach bulk cascade-like behavior, and the depth at which this occurs increases with E PKA , but is independent of temperature.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Quantitative Imaging of Cobalt Phthalocyanine Distribution on Carbon Nanotubes: A Deep Learning Approach to Catalyst Characterization

Electrochemical reduction of carbon dioxide (CO 2 ) offers a pathway to valuable products, with catalysts playing a crucial role. This study investigates the distribution of cobalt tetraaminophthalocyanine (CoPc-NH 2 ) immobilized on carbon nanotubes (CNTs), utilizing high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) to characterize CoPc-NH 2 distribution. A challenge in the quantitative HAADF-STEM analysis is the introduction of bias from manual Co atom identification. To address this, we developed and trained a convolutional neural network (CNN) using a data set generated from images of CoPc-NH 2 /CNT samples with varying Co loadings. The CNN, implemented in TensorFlow and Keras, facilitated Co atom detections. Analysis of the CNN-generated data confirmed a correlation between Co loading and surface density, consistent with findings from UV–vis spectroscopy. Furthermore, the application of Ripley’s L(d) function highlighted the presence of slight Co atom clustering. Furthermore, this work demonstrates the utility of the combined HAADF-STEM and CNN approach for providing spatially resolved information about catalyst distribution on nonplanar supports, revealing structural details that are typically lost through other characterization methods.

HAADF-STEM↗
DOE OSTI2025

Ultrafast Correlation Energy Estimator

A virtually no-cost method is proposed that can compute the correlation energies of general, covalently bonded, organic, and inorganic molecules (including conjugated π-electron systems) with a well-defined dominant Lewis structure at the accuracy of 99.5% of the near-exact values determined by the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] in the complete-basis-set (CBS) limit. This Correlation Energy Per Bond (CEPB) method assigns a partial correlation energy to each bond type (characterized by the identities of the two atoms forming the bond and its integer bond order) and to a lone pair, regardless of the bond length, bond angle, sp-hybridization, π-electron conjugation, ionicity, noncovalent interactions, etc. At its current stage, the method is mainly suitable for near-equilibrium geometries. The correlation energies per bond are determined by a fit to the CCSD(T)/CBS benchmarks. It can neither improve the equilibrium structures nor discern conformers or positional isomers, yet its accuracy for reaction energies rivals that of the second-order Møller–Plesset perturbation theory, which is far more expensive. Its promising performance underscores the possibility that surprisingly compact, chemically intuitive molecular fragments exist into which correlation energies can be partitioned, leading to various ultrafast correlation-energy estimators tailored to different purposes.

Binding energy↗
DOE OSTI2025

Gating Single Molecules with Counterions

We report atomic-scale gating and visualization of local charge distribution within individual rare-earth-based molecular complexes on a metallic surface. The complexes are formed by a positively charged lanthanum ion coordinated to a (pcam)3 molecule and a negatively charged counterion trapped underneath via electrostatic interactions on a Au(111) surface. Local gating is performed by adding an additional negatively charged counterion to one side of the complex, which results in the redistribution of charges within the complex and a positive shift of the frontier orbitals. This is caused by the internal Stark effect induced by the added counterion. This effect is directly captured using tunneling spectroscopy and spectroscopic mapping at 5 K substrate temperature. The polarizability of the complex is corroborated by density functional theory and analytical calculations based on experimental findings. Furthermore, the influence of charge polarization on nearby complexes is investigated in a cluster purposely assembled using three complexes, which reveals maintaining the charge states as in single complexes. These findings will enable the design of robust charged rare-earth complexes to be tailored for potential solid-state applications.

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

Simulation of multi-shell fullerenes using Machine-Learning Gaussian Approximation Potential

Multi-shell fullerenes ”buckyonions ” were simulated, starting from initially random configurations, using a density-functional-theory (DFT)-trained machine-learning carbon potential within the Gaussian Approximation Potential (GAP) Framework [Volker L. Deringer and Gábor Csányi, Phys. Rev. B 95, 094203 (2017)]. Fullerenes formed from seven different system sizes, ranging from 60 ~ 3774 atoms, were considered. The buckyonions are formed by clustering and layering starting from the outermost shell and proceeding inward. Inter-shell cohesion is partly due to interaction between delocalized π electrons protruding into the gallery. The energies of the models were validated ex post facto using density functional codes, VASP and SIESTA , revealing an energy difference within the range of 0.02 - 0.08 eV/atom after conjugate gradient energy convergence of the models was achieved with both methods.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Performant implementation of the atomic cluster expansion

The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code PACE that is suitable for use in large scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in PACE shifts a previously established Pareto front for machine learning interatomic potentials towards faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the new Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Ensembles of Metastable States Govern Heterogeneous Catalysis on Dynamic Interfaces

Heterogeneous catalysis is at the heart of chemical industry. Being able to tune and design efficient catalysts for processes of interest is of an utmost importance, and for this, the molecular-level understanding of heterogeneous catalysts is the first step, and indeed a prime focus of the modern catalysis research. For a long time, a single most thermodynamically stable structure of the catalytic interface attained in reaction conditions had been envisioned as the reactive phase. However, some catalytic interfaces continue to undergo structural dynamics in the steady state, triggered by high temperatures, pressures, and binding and changing reagents. Among particularly dynamic interfaces are such widely-used catalysts as crystalline and amorphous surfaced supporting (sub-)nano metallic clusters. Recently, it became clear that this dynamic fluxionality causes the supported clusters to populate many distinct structural and stoichiometric states in catalytic conditions. Hence, the catalytic interface should be viewed as an evolving statistical ensemble of many (not one) structures. As such, every member in the ensemble contributes to the properties of the catalyst differently, and in proportion to its probability to be populated. This new notion flips the established paradigm and calls for new theory, modeling approaches, operando measurements, and updated design strategies. The statistical ensemble nature of surface-supported sub-nano cluster catalysts can be exemplified by oxide-supported and adsorbate-covered Pt, Pd, Cu, CuPd clusters, catalytic toward oxidative and non-oxidative dehydrogenation. They have access to a variety of 3D and quasi-2D shapes. The compositions of their thermal ensembles are dependent on the cluster size, leading to size-specific catalytic activities and the famous “every atom counts” phenomenon. The support and adsorbates affect catalyst structures, and state of the reacting species causes the ensemble to change in every reaction intermediate. The most stable member of the ensemble dominates the thermodynamic properties of the corresponding intermediate, whereas the kinetics can be determined by more active but less populated metastable catalyst states, and that suggests that many earlier studies might have overlooked the actual active sites. Both effects depend on the relative time-scales of catalyst restructuring and reaction dynamics. The catalyst may routinely operate off-equilibrium. Ensemble phenomena lead to surprising exceptions from established rules of catalysis, such as scaling relations, and Arrhenius behavior. Catalyst deactivation is also an ensemble property, and its extent of mitigation can be predicted through the new paradigm. These findings were enabled by advances in theory, such as global optimization and subsequent utilization of multiple local minima, and pathways sampling, as well as operando catalyst characterization. The fact that the per-site and per-species resolution is needed for the description and predicting of catalyst properties gives theory the central role in catalysis research, as most experiments provide ensemble-average information and cannot detect the crucial minority species that may be responsible for the catalytic activity.

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

Ligand-Driven Electrochemical Tuning of Co 6 Se 8 Chevrel Clusters

Molecular “Chevrel-type” clusters of the formula Co 6 Se 8 L 6 (L = neutral ligand) are a well-studied class of clusters due to their utility as molecular analogues to the Chevrel extended solid phase and their application as subunits in hierarchical materials. However, their solution and optical properties remain relatively underexplored. Aiming to develop the fundamental relationships between the molecular and electronic structures of these clusters and their electrochemical and photophysical properties, this work reports the preparation of a series of Co 6 Se 8 (P­(C 6 H 4 R) 3 ) 6 -type clusters with R = Cl (1), F (2), H (3), CH 3 (4), and OCH 3 (5) via a stepwise synthetic approach. Solution and solid-state experimental characterization and density functional theory calculations reveal that the Co 6 Se 8 cores of 1–5 maintain consistent electronic and structural properties despite the variation of the triarylphosphine ligand para-substituent Hammett parameters (σ p ). However, cyclic voltammetry measurements indicate that the electron transfer energetics of 1–5 are strongly influenced by ligand substitution, with the E 1/2 of a given redox event spanning ∼0.5 V depending on the triarylphosphine ligand’s σ p . In conclusion, these findings support the characterization of Co 6 Se 8 clusters as atomically precise nanoclusters with both the structural robustness and the electrochemical tunability needed to act as components in larger charge transfer assemblies.

Wheaton, Amelia M. [Argonne National Laboratory (A↗
DOE OSTI2025

Morphology Effects on Free Energies of Proton-Coupled Electron Transfer in Polyoxotungstates

Polyoxotungstates have previously been established to facilitate the hydrogenation of small molecule substrates via hydrogen atom transfer from reactive hydroxyl groups formed at the assembly surface. Understanding structure−function relationships that dictate the thermochemistry and kinetics of protoncoupled electron transfer is key to controlling this chemistry. In this work, we combine comprehensive electrochemical experiments and density functional theory calculations to address how different polyoxotungstate morphologies, specifically W 6 O 19 −2 , W 10 O 32 −4 , SiW 12 O 40 −4 , and P 2 W 18 O 62 −6 , affect the bond dissociation free energies of surface hydroxides (BDFE(O−H)) formed upon reduction of the assembly in acidic media. Our results reveal increasing hydroxide bond strengths with increasing cluster size, and that anisotropic cluster geometries result in substantial thermodynamic differentiation of H-binding sites. We demonstrate an excellent agreement between theory and experiments on the reported BDFE(O−H) values and, importantly, we elucidate how cluster size and shape affect electronic properties (local charges and frontier molecular orbitals), giving rise to sites with increased preference for hydrogen binding, demonstrated in higher BDFE(O−H). Overall, this work aids the understanding and design of polyoxometalates exhibiting surface sites with tailored interaction strengths.

anions↗
NASA NTRS1994

Observations of ultraviolet-bright stars in globular clusters with the Hopkins Ultraviolet Telescope

Two UV-bright stars in globular clusters, UV5 in NGC 1851 and vZ 1128 in M3, were observed with the Hopkins Ultraviolet Telescope (HUT) during the Astro-1 space shuttle mission in 1990 December. The stars' spectra show weak absorption features and no significant emission features other than well known geocoronal lines. Detailed fitting of Kurucz (1991) stellar atmosphere models using a chi(sup 2) minimization technique indicates T(sub eff) = 16 000 K, log g = 2.5, and abundance (-1.0) (logarithm of abundance of elements heavier than helium relative to solar) for UV5, and T(sub eff) = 35 000 K, log g = 4.0, and abundance (-3.5) for vZ 1128. The Kurucz model which best fits vZ 1128 overpredicts the flux in the region below approximately 1000 A, an effect seen in previous models of O-type stars. Our results are robust (to within approximately 1000 K) with respect to uncertainties in interstellar reddening and atomic and molecular hydrogen column densities. We do not see significant molecular hydrogen absorption, which might have indicated material in a circumstellar shell, in either star's spectrum. We estimate the stellar luminosities to be log L/solar luminosity = 3.33 +/- 0.15 for UV5 and log L/solar luminosity = 3.21 +/- 0.12 for vZ 1128. These atmospheric parameters place both stars on the Schoenberner (post-AGB) tracks, though the stellar masses derived from the best-fitting Kurucz models are somewhat less than those predicted by the Schoenberner models. Examination of individual absorption line strengths reveals no significant abundance anomalies in either star.

Van Dyke Dixon, W.↗
NASA NTRS2011

A Laboratory and Theoretical Study of Silicon Hydroxide SiOH

The rotational spectrum of the triatomic free radical SiOH in its X 2A' ground electronic state has been observed in a supersonic molecular beam by Fourier transform microwave spectroscopy. The fundamental (10,1 yields 00,0) transition has been detected for normal SiOH and for three rare isotopic species: (30)SiOH, Si(18)OH, and SiOD. The same transition has also been observed in two of three excited vibrational states, v2 and v3, for the most abundant species. Precise spectroscopic constants, including those that describe the effective spin doubling and hydrogen hyperfine structure, have been derived for each isotopic species or vibrational state. To complement the laboratory work, theoretical calculations of the structure, dipole moment, and energies of the X 2A' and low-lying 1 2A'' states have also been undertaken at the coupled cluster level of theory. In agreement with theoretical predictions, we conclude from the hyperfine constants that SiOH is a best described as a pi-type radical, with the unpaired electron localized on a p orbital on the silicon atom. Assuming a bond angle of 118.5 deg, the Si-O bond length is 1.647(2) Angstroms and the O-H bond length is 0.969(4) Angstrom.

McCarthy, M. C.↗
DOE OSTI2021

Boson Fermion Nucleus And Previous Research On Alpha Clustering And Tetrahedral Structure In The Nucleus: Monograph #9

For 80 years, the presence of alpha clusters in nuclei and nuclei with tetrahedral structures has been studied in theory and researched in experiment. Scattering experiments have detected alpha clusters in heavy nuclei. The theoretical treatment of this evidence has considered close-packed alpha clusters bound together in stable nuclear structures throughout the periodic table. While alpha clusters have been conceived as linear two-dimensional and three-dimensional close-packed, crystal-like structures, theorists have not considered three-dimensional extended structures as exhibited by boson fermion nuclei (BFNs). BFNs are composed of alphas and the nuclei of hydrogen, deuterium, tritium, and helium-3 as building blocks. Previous theoretical and experimental work has shown correspondence with the 6 Li, 7 Li, 10 B, 11 B, and 40 Ca BFN.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2020

Three-Dimensional Patterning of Nanoparticles by Molecular Stamping

Directing the formation of nanoscale architectures from nanoparticles is one of the key challenges in designing nanomaterials with prescribed functions. Atomic systems, given their ability to form molecules and crystals via directional chemical bonds, provide an inspiration for establishing approaches where nanoparticles with designed anisotropic binding modalities can be assembled into nanoscale architectures. However, fabricating such nanoparticles has been challenging due to their small dimensions and limited ways for site-specific control of their surface. To this end, we present a Molecular Stamping (MOST) approach to pattern DNA-coated nanoparticles with molecules at the predefined positions on a nanoparticle surface. This patterning is realized by use of a rigid and coordinative DNA frame as a molecular stamping apparatus (MOST App). The MOST App transfers multiple types of molecular “inks”, DNA sequences, onto nanoparticle surface and fixes these molecular inks into place to form a designed pattern. After a nanoparticle release from MOST App, it possesses single-molecule patches that can provide anisotropic bonds with distinctive affinities. We further use these stamped nanoparticles to assemble prescribed clusters, whose structure is determined by the locations of patches. Using electron microscopy and tomographic methods, we investigate the efficiency of cluster formation and the resulting spatial arrangements of nanoparticles. The presented approach provides a single-molecule and spatiallydetermined control over nanoparticle functionalization for creating nanoparticles with designed placement of different molecules and for realizing a rational fabrication of nanomaterial architectures.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Early Career: First-Principles Tools for Nonadiabatic Attosecond Dynamics in Materials

The overarching goal of this project was to develop computer tools for predicting how electrons move in molecules and solids at the attosecond (billionth-of-a-billionth of a second) time scale, during and after interaction with intense and/or high energy laser light. An associated goal was to also determine how X-ray spectroscopy could be used as a probe of these dynamics. The project resulted in multiple methodology developments that allow for these processes to be simulated from first-principles, most notably the use of small bulk-mimicking clusters to model solids and fixes for a deficiency in a commonly used method (time-dependent density functional theory). Additionally, the simulations showed that X-ray absorption peaks can be directly related to the electron density above the absorbing atom, and can thus be used as an intuitive probe of "where the electrons are" at a given time in the system. Collectively, these tools and results expected to be valuable for predicting and interpreting future attosecond experiments, especially for X-ray pump/probe studies at free-electron laser facilities.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Molecular dynamics simulations of radiation cascade evolution near cellular dislocation structures in additively manufactured stainless steels

The dislocation dense cellular structures observed in additively manufactured (AM) stainless steels can allow these materials to have enhanced strength and ductility compared to conventionally manufactured materials. Effective design of radiation resistant materials often necessitates creating microstructures containing of a high density of dislocations that act as sinks for radiation induced defects. This work uses molecular dynamics simulations to study the impact of pre-existing defects on radiation damage in stainless steel 316L fabricated by the laser powder bed fusion process. The evolution of synthetically generated dislocations in a crystal system in response to multiple radiation collision cascades suggest that dislocation dense regions reduce the probability of surviving point defects forming clusters. This finding seems to result from the dislocation cores’ ability to absorb point defects, thereby limiting the formation of clusters during the recombination phase. However, after successive cascades, the ability of the dislocation entanglement to prevent defect formation is diminished and defect cluster formation trends to an equilibrium. Accordingly, it is hypothesized that in an experimental setting the dislocation cells will initially act as neutral sinks for point defects, potentially delaying the onset of radiation damage effects; but, these structures will be degraded due to radiation-enhanced diffusion and lose their effectiveness at doses above 1.5–2 displacements per atom. Nevertheless, the ability to produce complex and feature-specific microstructures suggests promise for the design of radiation tolerant materials using AM methods.

36 MATERIALS SCIENCE↗
DOE OSTI2024

ELECTRONIC STRUCTURE METHODS AND PROTOCOLS WITH APPLICATION TO DYNAMICS, KINETICS AND THERMOCHEMISTRY

Hydrocarbon combustion involves the reaction dynamics of a tremendous number of species beginning with many-component fuel mixtures and proceeding via a complex system of intermediates to form primary and secondary products. Combustion conditions corresponding to new advanced engines and/or alternative fuels rely increasingly on autoignition and low-temperature-combustion chemistry. In these regimes various transient radical species such as HO2, ROO·, ·QOOH, HCO, NO2, HOCO, and Criegee intermediates play important roles in determining the detailed as well as more general dynamics. A clear understanding and accurate representation of these processes is needed for effective modeling. Given the difficulties associated with making reliable experimental measurements of these systems, computation can play an important role in developing these energy technologies. Accurate calculations have their own challenges since even within the simplest dynamical approximations such as transition state theory, the rates depend exponentially on critical barrier heights and these may be sensitive to the level of quantum chemistry. Moreover, it is well-known that in many cases it is necessary to go beyond statistical theories and consider the dynamics. Quantum tunneling, resonances, radiative transitions, and non-adiabatic effects governed by spin-orbit or derivative coupling can be determining factors in those dynamics. Building upon progress made during a period of prior support through the DOE Early Career Program, this project combines developments in the areas of potential energy surface (PES) fitting and multistate multireference quantum chemistry to allow spectroscopically and dynamically/kinetically accurate investigations of key molecular systems (such as those mentioned above), many of which are radicals with strong multireference character and have the possibility of multiple electronic states contributing to the observed dynamics. An ongoing area of investigation is to develop general strategies for robustly convergent electronic structure theory for global multichannel reactive surfaces including diabatization of energy and other relevant surfaces such as dipole transition. Combining advances in ab initio methods with automated interpolative PES fitting allows the construction of high-quality PESs (incorporating thousands of high-level data) to be done rapidly through parallel processing on high-performance computing (HPC) clusters. In addition, new methods and approaches to electronic structure theory will be developed and tested through applications. This project will explore limitations in traditional multireference calculations (e.g., MRCI) such as those imposed by internal contraction, lack of high-order correlation treatment and poor scaling. Methods such as DMRG-based extended active-space CASSCF and various Quantum Monte Carlo (QMC) methods will be applied (including VMC/DMC and FCIQMC). Insight into the relative significance of different orbital spaces and the robustness of application of these approaches on leadership class computing architectures will be gained. Synergy with other components of this research program such as automated PES fitting and multireference quantum chemistry will be used to address challenges encountered by the standard approaches to computational thermochemistry (those being single-reference quantum chemistry and perturbative treatments of the anharmonic vibrational energy, which break down for some cases of electronic structure or floppy strongly coupled vibrational modes).

74 ATOMIC AND MOLECULAR PHYSICS↗