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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
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 OSTI2019

The Partition Function of the Four-Vertex Model in a Special External Field

The exactly solvable four-vertex model on a square grid with the fixed boundary conditions in a presence of a special external field is considered. Namely, we study a system in a linear field acting on the central column of the grid. The partition function of the model is calculated by the quantum inverse scattering method. The answer is written in determinantal form.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Semiclassical limits of quantum partition functions on infinite graphs

We prove that if H denotes the operator corresponding to the canonical Dirichlet form on a possibly locally infinite weighted graph (X, b, m), and if v : X → ℝ is such that H + v/ħ is well-defined as a form sum for all ħ > 0, then the quantum partition function tr(e{sup −βħ(H+v/ħ)}) converges to ∑{sub x∈X}e{sup −βv(x)} as ħ → 0 +, for all β > 0, regardless of the fact whether e{sup −βv} is a priori summable or not. This fact can be interpreted as a semiclassical limit, and it allows geometric Weyl-type convergence results. We also prove natural generalizations of this semiclassical limit to a large class of covariant Schrödinger operators that act on sections in Hermitian vector bundle over (X, m, b), a result that particularly applies to magnetic Schrödinger operators that are defined on (X, m, b)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. IV. Performance of many-body force fields and tight-binding schemes for the fluid phases of silicon

We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%–15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. III. Impact of combining rules on mixtures properties

Combining rules, such as the Lorentz-Berthelot rules, are routinely used to calculate the thermodynamic properties of mixtures using molecular simulations. Here we extend the expanded Wang-Landau simulation approach to determine the impact of the combining rules on the value of the partition function of binary systems, and, in turn, on the phase coexistence and thermodynamics of these mixtures. We study various types of mixtures, ranging from systems of rare gases to biologically and technologically relevant mixtures, such as water-urea and water-carbon dioxide. Comparing the simulation results to the experimental data on mixtures of rare gases allows us to rank the performance of combining rules. We find that the widely used Lorentz-Berthelot rules exhibit the largest deviations from the experimental data, both for the bulk and at coexistence, while the Kong and Waldman-Hagler provide much better alternatives. In particular, in the case of aqueous solutions of urea, we show that the use of the Lorentz-Berthelot rules has a strong impact on the Gibbs free energy of the solute, overshooting the value predicted by the Waldman-Hagler rules by 7%. This result emphasizes the importance of the combining rule for the determination of hydration free energies using molecular simulations.

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

Prototype equation of state for phase transition of confined fluids based on the generalized van der Waals partition function

A simple self-consistent prototype equation of state (EOS) based on the Generalized van der Waals (vdW) partition function has been demonstrated to describe the phase transition of simple fluids in nanopores with uniform size. Different from those commonly presented in the literature, the new EOS does not need an auxiliary equation that is conventionally applied to provide the capillary pressure derived from surface tension. Lastly, the encouraging performance of the EOS calls for further extension to applications with more complex fluids and porous media.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Experimental energy levels and partition function of the {sup 12}C{sub 2} molecule

The carbon dimer, the {sup 12}C{sub 2} molecule, is ubiquitous in astronomical environments. Experimental-quality rovibronic energy levels are reported for {sup 12}C{sub 2}, based on rovibronic transitions measured for and among its singlet, triplet, and quintet electronic states, reported in 42 publications. The determination utilizes the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The 23,343 transitions measured experimentally and validated within this study determine 5699 rovibronic energy levels, 1325, 4309, and 65 levels for the singlet, triplet, and quintet states investigated, respectively. The MARVEL analysis provides rovibronic energies for six singlet, six triplet, and two quintet electronic states. For example, the lowest measurable energy level of the a{sup 3}Π{sub u} state, corresponding to the J = 2 total angular momentum quantum number and the F {sub 1} spin-multiplet component, is 603.817(5) cm{sup −1}. This well-determined energy difference should facilitate observations of singlet–triplet intercombination lines, which are thought to occur in the interstellar medium and comets. The large number of highly accurate and clearly labeled transitions that can be derived by combining MARVEL energy levels with computed temperature-dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements. The experimental rovibronic energy levels, augmented, where needed, with ab initio variational ones based on empirically adjusted and spin–orbit coupled potential energy curves obtained using the Duo code, are used to obtain a highly accurate partition function, and related thermodynamic data, for {sup 12}C{sub 2} up to 4000 K.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

A new adsorption model based on generalized van der Waals partition function for the description of all types of adsorption isotherms

A new adsorption model is proposed based on the Generalized van der Waals partition function by introducing the concept of attractive region, which integrates the effects of the adsorption sites of adsorbent and represents pore space where adsorbates concentrate. A theoretical expression for the chemical potential of adsorbates in the attractive region is derived and used to calculate the adsorbate density in each attractive region. The model can generate all the six types of isotherms classified by the International Union of Pure and Applied Chemistry (IUPAC) report including those with hysteresis and is easy to use. It is a generalized model that can be applied to various types of porous materials. With the fitted parameters, the model can predict the adsorption isotherms even for adsorbents with wide pore size distributions. It also well captures the isotherm-type transition as temperature changes and can estimate the hysteresis when capillary condensation exists.

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

The large- N partition function for non-parity-invariant Chern-Simons-matter theories

We extend the Fermi gas approach to a class of ABJM-like necklace quiver theories without parity invariance. The resulting partition function on S 3 retains the form of an Airy function, but now includes a phase that scales as Nk in the large- N limit where k is an overall Chern-Simons level. We demonstrate the presence of this phase both analytically and numerically in the case of a three node quiver.

Supersymmetric Gauge Theory↗
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 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↗