Search NASA⌕ Search

SEARCH · Search NASA

Results for “PARTITION FUNCTION”

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

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

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A new approach to include electron interaction effects in super transition array opacity theory

A method is presented for the improved calculation of super-shell partition functions which include the repulsive electron–electron interaction energy terms in the Boltzmann factor. Heretofore these interaction terms were approximately treated via the use of Feynman–Jensen inequalities. Further, such investigations are of particular interest for the super-transition-array approach of hot-plasma radiative opacity.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Comparison of atomized mass and crater volume in laser ablation

The extent and dynamics of laser ablation are typically studied using crater imaging or by invoking the relationship between atomic emission and the mass removed. The former is a static view of a dynamic process and requires the accumulation of multiple shots in one location. The latter is complex and not absolute without calibration of the optical system with a standard of spectral radiance. We measure the mass of the atomized plume by laser atomic-absorption spectroscopy at 2 µs without external mass calibration; mass uncertainty in laser-ablation atomic absorption spectroscopy (LA-AAS) results from uncertainties in line area fitting, tabulated oscillator strengths, and partition functions as well as a <10% underrepresentation of the mass due to treating the plasma as a single thermodynamic equilibrium. The LA-AAS-measured mass pertains to the atoms in the probed charge states and does not include condensed or molecular species. The ablation efficiency at 300 mbar of helium varies significantly between the two focusing conditions used. A comparison of crater-derived masses and LA-AAS masses suggests that more defocused ablation may result in significant redeposition of material in the crater, distorting the conclusions from drilling studies and crater imaging. More focused ablation conditions result in crater-derived masses that exceed those measured with LA-AAS and suggest melt expulsion or phase explosion.

Merten, Jonathan [Arkansas State University, Jones↗
DOE OSTI2021

Phase transition to blob-hole coherent structure in the Hasegawa–Mima model for plasmas

An equilibrium statistical mechanics theory for the Hasegawa–Mima equations of toroidal plasmas, with canonical constraint on energy and microcanonical constraint on potential enstrophy, is solved exactly as a spherical model. The use of a canonical energy constraint instead of a fixed-energy microcanonical approach is justified by the preference for viewing real plasmas as an open system. A significant consequence of the results obtained from the partition function, free energy and critical temperature, is the condensation into a ground state exhibiting a blob-hole-like structure observed in real plasmas.

Physics↗
DOE OSTI2021

Entanglement Effect and Angular Momentum Conservation in a Nonseparable Tunneling Treatment

The important, and often dominant, role of tunneling in low temperature kinetics has resulted in numerous theoretical explorations into the methodology for predicting it. Nevertheless, there are still key aspects of the derivations that are lacking, particularly for nonseparable systems in the low temperature regime, and further explorations of the physical factors affecting the tunneling rate are warranted. In this work we obtain a closed-form rate expression for the tunneling rate constant that is a direct analog of the rigid-rotor-harmonic-oscillator expression. This expression introduces a novel "entanglement factor" that modulates the reaction rate. Furthermore, we are able to extend this expression, which is valid for nonseparable systems at low temperatures, to properly account for the conservation of angular momentum. In contrast, previous calculations have considered only vibrational transverse modes and so effectively employ a decoupled rotational partition function for the orientational modes. We also suggest a simple theoretical model to describe the tunneling effects in the vicinity of the crossover temperature (the temperature where tunneling becomes the dominating mechanism). This model allows one to naturally classify, interpret, and predict experimental data. Among other things, it quantitatively explains in simple terms the so-called "quantum bobsled" effect, also known as the negative centrifugal effect, which is related to curvature of the reaction path. Taken together, the expressions obtained here allow one to predict the thermal and E-resolved rate constants over broad ranges of temperatures and energies.

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

Reaction Energetics and 13 C Fractionation of Alanine Transamination in the Aqueous and Gas Phases

The alanine transaminase enzyme catalyzes the transfer of an amino group from alanine to α-ketoglutarate to produce pyruvate and glutamate. Isotope fractionation factors (IFFs) for the reaction +H 3 NCH(CH 3 )COO – + – OOCCH 2 CH 2 C(O)COO – ↔ CH 3 C(O)COO – + + H 3 NCH(CH 2 CH 2 COO – )COO – (zwitterionic neutral alanine + doubly deprotonated α-ketoglutarate ↔ pyruvate + zwitterionic glutamate anion) were calculated from the partition functions of explicitly and implicitly solvated molecules at 298 K. Calculations were done for alanine (noncharge separated, zwitterion, deprotonated), pyruvic acid (neutral, deprotonated), glutamic acid (noncharge separated, zwitterion, deprotonated, doubly deprotonated), and α-ketoglutaric acid (neutral, deprotonated, doubly deprotonated). The computational results, calculated from gas phase- and aqueous-optimized clusters with explicit H 2 O molecules at the MP2/aug-cc-pVDZ and MP2/aug-cc-pVDZ/COSMO levels, respectively, predict that substitution of 13 C at the C2 position of alanine and pyruvic acid and their various forms leads to the C2 position of pyruvic acid/pyruvate being enriched in 13 C/ 12 C ratio by 9‰. Simpler approaches that estimate the IFFs based solely on changes in the zero-point energies (ZPEs) are consistent with the higher-level model. ZPE-based IFFs calculated for simple analogues formaldehyde and methylamine (analogous to the C2 positions of pyruvate and alanine, respectively) predict a 13 C enrichment in formaldehyde of 7–8‰ at the MP2/aug-cc-pVDZ and aug-cc-pVTZ levels. A simple predictive model using canonical functional group frequencies and reduced masses for 13 C exchange between R 2 C=O and R 2 CH–NH 2 predicted enrichment in R 2 C=O that is too large by a factor of two but is qualitatively accurate compared with the more sophisticated models. Our models are all in agreement with the expectation that pyruvate and formaldehyde will be preferentially enriched in 13 C because of the strength of their >C=O bond relative to that of ≡C–NH 2 in alanine and methylamine. 13 C/ 12 C substitution is also modeled at the methyl and carboxylic acid sites of alanine and pyruvic acid, respectively.

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

Using Hyperoptimized Tensor Networks and First-Principles Electronic Structure to Simulate the Experimental Properties of the Giant {Mn 84 } Torus

The single-molecule magnet {Mn 84 } is a challenge to theory because of its high nuclearity. Here, we directly compute two experimentally accessible observables, the field-dependent magnetization up to 75 T and the temperature-dependent heat capacity, using parameter-free theory. In particular, we use first-principles calculations to derive short- and long-range exchange interactions and compute the exact partition function of the resulting classical Potts and Ising spin models for all 84 Mn S = 2 spins to obtain observables. The latter computation is made possible by using hyperoptimized tensor network contractions, a technique developed to simulate quantum supremacy circuits. We also synthesize the magnet and measure its heat capacity and magnetization, observing qualitative agreement between theory and experiment and identifying an unusual bump in the heat capacity and a plateau in the magnetization. Our work also identifies some limitations of current theoretical modeling in large magnets, such as sensitivity to small, long-range exchange couplings.

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

Phase Transition and Criticality of Methane Confined in Nanopores

For the first time, the phase transition and criticality of methane confined in nanoporous media are measured. The measurement is performed by establishing an experimental setup utilizing a differential scanning calorimeter (DSC) capable of operating under very low temperatures as well as high pressures to detect the capillary phase transition of methane inside nanopores. By performing experiments along isochoric cooling paths, both the capillary condensation and the bulk condensation of methane are detected. Here, the pore critical point (PCP) of nanoconfined methane is also determined and then used to derive the parameters of a previously developed self-consistent equation of state based on the Generalized van der Waals (vdW) partition function. Using this parameter, the equation of state can predict the capillary-condensation curves that agree well with the experimental data.

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

Kinetics of the benzyl + HO 2 and benzoxyl + OH barrierless association reactions: fate of the benzyl hydroperoxide adduct under combustion and atmospheric conditions

Radical–radical association reactions are challenging to address theoretically due to difficulties finding the bottleneck that variationally minimizes the reactive flux. For this purpose, the variable reaction coordinate (VRC) formulation of the variational transition state theory (VTST) represents an appropriate tool. Here, we revisited the kinetics of two radical–radical association reactions of importance in combustion modelling and poly-aromatic hydrocarbon (PAH) chemistry by performing VRC calculations: benzyl + HO 2 and benzoxyl + OH, both forming the adduct benzyl hydroperoxide. Our calculated rate constants are significantly lower than those previously reported based on VTST calculations, which results from a more efficient minimization of the reactive flux through the bottleneck achieved by the VRC formulation. Both reactions show different trends in the variation of their rate constants with temperature. We observed that if the pair of single occupied molecular orbitals (SOMOs) of the associating radicals show a similar nature, i.e. similar character, and thereby a small energy gap, a highly stabilized transition state structure is formed as the result of a very efficient SOMO–SOMO overlap, which may cancel out the free energy bottleneck for the formation of the adduct and result in large rate constants with a negative temperature dependence. This is the case of the benzoxyl and OH radical pair, whose SOMOs show O 2p nature with an energy gap of 20.2 kcal mol –1 . On the other hand, the benzyl and HO 2 radical pair shows lower rate constants with a positive temperature dependence due to the larger difference between both SOMOs (a 28.9 kcal mol –1 energy gap) as a consequence of the contribution of the multiple resonance structures of the benzyl radical. The reverse dissociation rate constants were also calculated using multi-structural torsional anharmonicity partition functions, which were not included in previous work, and the results show a much slower dissociation of benzyl hydroperoxide. Our work may help to improve kinetic models of interest in combustion and PAH formation, as well as to gain further understanding of radical–radical association reactions, which are ubiquitous in different environments.

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

A quantitative model for a nanoscale switch accurately predicts thermal actuation behavior

Manipulation of temperature can be used to actuate DNA origami nano-hinges containing gold nanoparticles. We develop a physical model of this system that uses partition function analysis of the interaction between the nano-hinge and nanoparticle to predict the probability that the nano-hinge is open at a given temperature. The model agrees well with experimental data and predicts experimental conditions that allow the actuation temperature of the nano-hinge to be tuned over a range of temperatures from 30 °C to 45 °C. Additionally, the model identifies microscopic interactions that are important to the macroscopic behavior of the system, revealing surprising features of the system. This combination of physical insight and predictive potential is likely to inform future designs that integrate nanoparticles into dynamic DNA origami structures or use strand binding interactions to control dynamic DNA origami behavior. Furthermore, our modeling approach could be expanded to consider the incorporation, stability, and actuation of other types of functional elements or actuation mechanisms integrated into nucleic acid devices.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Surface phase diagrams from nested sampling

From nested sampling, we compute the partition function and, from that, the phase diagram of gas adsorbates, including their anharmonic and configurational degrees of freedom, on flat and stepped surfaces of the Lennard-Jones solid.

Chemistry↗
DOE OSTI2025

Accurate and reliable thermochemistry by data analysis of complex thermochemical networks using Active Thermochemical Tables: the case of glycine thermochemistry

Active Thermochemical Tables (ATcT) were successfully used to resolve the existing inconsistencies related to the thermochemistry of glycine, based on statistically analyzing and solving a thermochemical network that includes >3350 chemical species interconnected by nearly 35 000 thermochemically-relevant determinations from experiment and high-level theory. Here, the current ATcT results for the 298.15 K enthalpies of formation are −394.70 ± 0.55 kJ mol −1 for gas phase glycine, −528.37 ± 0.20 kJ mol −1 for solid α-glycine, −528.05 ± 0.22 kJ mol −1 for β-glycine, −528.64 ± 0.23 kJ mol −1 for γ-glycine, −514.22 ± 0.20 kJ mol −1 for aqueous undissociated glycine, and −470.09 ± 0.20 kJ mol −1 for fully dissociated aqueous glycine at infinite dilution. In addition, a new set of thermophysical properties of gas phase glycine was obtained from a fully corrected nonrigid rotor anharmonic oscillator (NRRAO) partition function, which includes all conformers. Corresponding sets of thermophysical properties of α-, β-, and γ-glycine are also presented.

Active Thermochemical Tables↗
DOE OSTI2020

The role of rotation-vibration coupling in symmetric and asymmetric isotopomers of ozone

A theoretical framework and a computer code (SpectrumSDT) are developed for accurate calculations of coupled rotational–vibrational states in triatomic molecules using hyper-spherical coordinates and taking into account the Coriolis coupling effect. Concise final formulas are derived for the construction of the Hamiltonian matrix using an efficient combination of the variational basis representation and discrete variable representation methods with locally optimized basis sets and grids. First, the new code is tested by comparing its results with those of the APH3D program of Kendrick et al. [Kendrick, Pack, Walker, and Hayes, J. Chem. Phys. 110, 6673 (1999)]. Then, accurate calculations of the rovibrational spectra are carried out for doubly substituted symmetric ( 18 O 16 O 18 O) and asymmetric ( 18 O 18 O 16 O) ozone isotopomers for the total angular momentum up to J = 5. Together with similar data recently reported for the singly substituted symmetric ( 16 O 18 O 16 O) and asymmetric ( 16 O 16 O 18 O) ozone isotopomers, these calculations quantify the role of the Coriolis coupling effect in the large mass-independent isotopic enrichment of ozone, observed in both laboratory experiments and the atmosphere of the Earth. It is found that the Coriolis effect in ozone is relatively small, as evidenced by deviations of its rotational constants from the symmetric-top-rotor behavior, magnitudes of parity splittings (Λ-doubling), and ratios of rovibrational partition functions for asymmetric vs symmetric ozone molecules. It is concluded that all of these characteristics are influenced by the isotopic masses as much as they are influenced by the overall symmetry of the molecule. It is therefore unlikely that the Coriolis coupling effect could be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes in ozone.

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

On the Cauchy problem for Boltzmann equation modeling a polyatomic gas

In the present article, we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the space homogeneous setting for the full non-linear case, under an extended Grad-type assumption on transition probability rates, which comprises hard potentials for both the relative speed and internal energy with the rate in the interval 0,2, multiplied by an integrable angular part and integrable partition functions. The Cauchy problem is resolved by means of an abstract ordinary differential equation (ODE) theory in Banach spaces for the initial data with finite and strictly positive gas mass and energy, finite momentum, and additionally finite K* polynomial moment, with K* depending on the rate of the transition probability and the structure of a polyatomic molecule or its internal degrees of freedom. Moreover, we prove that polynomially and exponentially weighted Banach space norms associated with the solution are both generated and propagated uniformly in time.

Physics↗
DOE OSTI2024

Computing equilibrium free energies through a nonequilibrium quench

Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper [G. M. Rotskoff and E. Vanden-Eijnden, Phys. Rev. Lett. 122, 150602 (2019)] demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium “quench” process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here, we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of N-independent harmonic springs and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling. We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications.

Chemistry↗
DOE OSTI2022

Baby universes and worldline field theories

The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra of quantum fields, while the former has been argued to define an abelian algebra of superselected observables associated with partition-function-like quantities at an asymptotic boundary. We resolve this apparent tension by pointing out a variety of discrete choices that must be made in constructing a Hilbert space from such path integrals, and arguing that the natural choices for quantum gravity differ from those used to construct QFTs. We focus on one-dimensional models of quantum gravity in order to make direct comparisons with worldline QFT. Finally, we also restrict attention to models in which worldlines do not split apart or join together.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

AdS 3 Einstein gravity and boundary description: pedagogical review

We review the various aspects of the 3D Einstein gravity theory with a negative cosmological constant and its boundary description. We also explore its connections to conformal field theories (CFTs), modular symmetry, and holography. It is worth noting that this particular theory is topological in nature, which means that all the physical degrees of freedom are located on the boundary. Additionally, we can derive the boundary description on a torus, which takes the form of a 2D Schwarzian theory. This observation suggests that the relevant degrees of freedom for the theory can be described using this 2D theory. Because of the renormalizability of the 3D gravity theory, one can probe the quantum regime. This suggests that it is possible to investigate quantum phenomena. Unlike the conventional CFTs, when considering the AdS 3 background, the boundary theory loses modular symmetry. This represents a departure from the usual behavior of CFT and is quite intriguing. The Weyl transformation induces anomaly in CFTs, and we indicate that applying this transformation to the 2D Schwarzian theory leads to similar results. Summing over all geometries with the asymptotic AdS 3 boundary condition is equivalent to summing over a modular group. The partition function is one-loop exact and therefore an analytical expression from the summation. This theory holds potential applications in Quantum Information and is a recurring theme in the study of holography, where gravitational theories are connected with CFTs.

2D Schwarzian theory↗
DOE OSTI2024

The Einstein–Hilbert action for entropically dominant causal sets

Abstract In the path integral formulation of causal set quantum gravity, the quantum partition function is a phase-weighted sum over locally finite partially ordered sets, which are viewed as discrete quantum spacetimes. It is known, however, that the number of ‘layered’ sets—a class of causal sets that look nothing like spacetime manifolds—grows superexponentially with the cardinalityn, giving an entropic contribution that can potentially dominate that of the action. We show here that in any dimension, the discrete Einstein–Hilbert action for a typicalK-layered causal set reduces to the simple link action to leading order inn. Combined with earlier work, this completes the proof that the layered sets, although entropically dominant, are very strongly suppressed in the path sum of causal set quantum gravity whenever the discreteness scale is greater than or equal to a (mildly dimension-dependent) order one multiple of the Planck scale.

Astronomy & Astrophysics↗