Search NASA⌕ Search

SEARCH · Search NASA

Results for “HARMONIC POTENTIAL”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An asymptotic approach for the statistical thermodynamics of certain model systems

In classical statistical thermodynamics, calculating the configuration integral is both vital and elusive. Analytic relations for configuration integrals are desirable for modeling purposes, but it is typically impossible to obtain them. Certain systems become analytically tractable after replacing steep potential energies with harmonic potentials or athermal rigid constraints, but these approximations are often inadequate, especially when modeling the stretching of molecules. It is therefore necessary to develop a systematic approach to improve upon the approximations provided by these reference systems. Here, a general asymptotic approach is introduced, where the configuration integral for the full system is obtained in terms of that of the reference system and several corrections. This asymptotic approach is first demonstrated using the simple example of a classical three-dimensional oscillator. Next, the approach is applied to modeling the stretching of single polymer chains and to modeling thermally assisted crack growth, where results are verified with respect to numerical calculations. Overall, this asymptotic approach is a valid and effective tool for statistical thermodynamics in general.

Buche, Michael Robert↗
DOE OSTI2021

Spatiotemporal spread of perturbations in power-law models at low temperatures: Exact results for classical out-of-time-order correlators

Here, we present exact results for the classical version of the out-of-time-order commutator (OTOC) for a family of power-law models consisting of N particles in one dimension and confined by an external harmonic potential. These particles are interacting via power-law interaction of the form ∝ $Σ_{i,j=(i≠j)}^{N}$ |x i -x j | -k for every k>1 where x i is the position of the i th particle. We present numerical results for the OTOC for finite N at low temperatures and short enough times so that the system is well approximated by the linearized dynamics around the many-body ground state. In the large-N limit, we compute the ground-state dispersion relation in the absence of external harmonic potential exactly and use it to arrive at analytical results for OTOC. We find excellent agreement between our analytical results and the numerics. We further obtain analytical results in the limit where only linear and leading nonlinear (in momentum) terms in the dispersion relation are included. The resulting OTOC is in agreement with numerics in the vicinity of the edge of the “light cone.” We find remarkably distinct features in OTOC below and above k=3 in terms of going from non-Airy behavior (1 < k < 3) to an Airy universality class (k>3). We present certain additional rich features for the case k=2 that stem from the underlying integrability of the Calogero-Moser model. We present a field theory approach that also assists in understanding certain aspects of OTOC such as the sound speed. Our findings are a step forward towards a more general understanding of the spatiotemporal spread of perturbations in long-range interacting systems.

1-dimensional systems↗
DOE OSTI2024

Quantum Liouville theorem based on Haar measure

Liouville theorem (L theorem) reveals robust incompressibility of the distribution function in phase space, given arbitrary potentials. However, its quantum generalization, Wigner flow, is compressible, i.e., L theorem is only conditionally true (e.g., for perfect Harmonic potential). Here, we develop quantum L theorem (rigorous incompressibility) for arbitrary potentials (interacting or not) in Hamiltonians. Haar measure, instead of symplectic measure dp$\bigwedge$dq used in Wigner’s scheme, plays a central role. The argument is based on general measure theory, independent of specific spaces or coordinates. Comparison of classical and quantum is made: for instance, here we address why Haar measure and metric preservation do not work in the classical case. Applications of the theorems in statistics, topological phase transition, ergodic theory, etc., are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Extended molecular eigenmodes treatment of dipole–dipole NMR relaxation in real fluids

Traditional models of NMR relaxation fail to account for the complex, multi-exponential behavior of the autocorrelation function in realistic systems characterized by soft-interactions and molecules that are chemically and physically complex. Here, in this study, we describe the relative diffusion of the spin dipoles by means of a Fokker–Planck equation that includes an interaction potential of mean force to account for the response of the physical/chemical environment around the dipoles. By numerically solving the Fokker–Planck equation for the diffusion propagator, we estimate dipole–dipole NMR relaxation for like- and unlike-spin systems via its eigenmode solution. We test the model against molecular simulations of diffusing dipoles with harmonic potentials and also validate using experimental longitudinal relaxation data from real systems, including Gd(III)–aqua and Gd(III)–DO3A–butrol complexes, the latter being an important MRI contrast agent. Using this novel approach, we predict both the inner- and outer-shell contributions to the relaxivity rates with excellent accuracy at frequencies relevant to MRI. We also show that, under the appropriate assumptions, our framework naturally recovers the Bloembergen–Purcell–Pound, the Solomon–Bloembergen–Morgan, and the Hwang–Freed models. Our implementation is general and publicly available for application to a broad range of systems.

Pinheiro dos Santos, Thiago J. [Rice Univ., Housto↗
DOE OSTI2022

Causality and dimensionality in geometric scattering

We report the scattering matrix which describes low-energy, non-relativistic scattering of spin-1/2 fermions interacting via finite-range potentials can be obtained from a geometric action principle in which space and time do not appear explicitly. In the case of zero-range forces, causality leads to constraints on scattering trajectories in the geometric picture. The effect of spatial dimensionality is also investigated by considering scattering in two and three dimensions. In the geometric formulation it is found that dimensionality is encoded in the phase of the harmonic potential that appears in the geometric action.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Bonding and Acidity of the Formal Hydride in the Prototypical Au 9 (PPh 3 ) 8 H 2+ Nanocluster

Abstract The role of hydrogen atoms as surface ligands on metal nanoclusters is of profound importance but remains difficult to directly study. While hydrogen atoms often appear to be incorporated formally as hydrides, evidence suggests that they donate electrons to the cluster's delocalized superatomic orbitals and may consequently behave as acidic protons that play key roles in synthetic or catalytic mechanisms. Here we directly test this assertion for the prototypical Au 9 (PPh 3 ) 8 H 2+ nanocluster, formed by addition of a hydride to the well‐characterized Au 9 (PPh 3 ) 8 3+ . Using gas‐phase infrared spectroscopy, we were able to unambiguously isolate Au 9 (PPh 3 ) 8 H 2+ and Au 9 (PPh 3 ) 8 D 2+ , revealing an Au−H stretching mode at 1528 cm −1 that shifts to 1038 cm −1 upon deuteration. This shift is greater than the maximum expected for a typical harmonic potential, suggesting a potential governing cluster‐H bonding that has some square‐well character consistent with the hydrogen nucleus behaving as a metal atom in the cluster core. Complexing this cluster with very weak bases reveals a redshift of 37 cm −1 in the Au−H vibration, consistent with those typically seen for moderately acidic groups in gas phase molecules and providing an estimate of the acidity of Au 9 (PPh 3 ) 8 H 2+ , at least with regard to its surface reactivity.

Hernández, Hanna Morales↗
DOE OSTI2023

Bonding and Acidity of the Formal Hydride in the Prototypical Au 9 (PPh 3 ) 8 H 2+ Nanocluster

The role of hydrogen atoms as surface ligands on metal nanoclusters is of profound importance but remains difficult to directly study. While hydrogen atoms often appear to be incorporated formally as hydrides, evidence suggests that they donate electrons to the cluster's delocalized superatomic orbitals and may consequently behave as acidic protons that play key roles in synthetic or catalytic mechanisms. Here we directly test this assertion for the prototypical Au 9 (PPh 3 ) 8 H 2+ nanocluster, formed by addition of a hydride to the well-characterized Au 9 (PPh 3 ) 8 3+ . Using gas-phase infrared spectroscopy, we were able to unambiguously isolate Au 9 (PPh 3 ) 8 H 2+ and Au 9 (PPh 3 ) 8 D 2+ , revealing an Au–H stretching mode at 1528 cm –1 that shifts to 1038 cm –1 upon deuteration. This shift is greater than the maximum expected for a typical harmonic potential, suggesting a potential governing cluster-H bonding that has some square-well character consistent with the hydrogen nucleus behaving as a metal atom in the cluster core. Complexing this cluster with very weak bases reveals a redshift of 37 cm –1 in the Au–H vibration, consistent with those typically seen for moderately acidic groups in gas phase molecules and providing an estimate of the acidity of Au 9 (PPh 3 ) 8 H 2+ , at least with regard to its surface reactivity.

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

Pynta-An Automated Workflow for Calculation of Surface and Gas-Surface Kinetics

Many important industrial processes rely on heterogeneous catalytic systems. However, given all possible catalysts and conditions of interest, it is impractical to optimize most systems experimentally. Automatically generated microkinetic models can be used to efficiently consider many catalysts and conditions. However, these microkinetic models require accurate estimation of many thermochemical and kinetic parameters. Manually calculating these parameters is tedious and error prone, involving many interconnected computations. Here, we present Pynta, a workflow software for automating the calculation of surface and gas–surface reactions. Pynta takes the reactants, products, and atom maps for the reactions of interest, generates sets of initial guesses for all species and saddle points, runs all optimizations, frequency, and IRC calculations, and computes the associated thermochemistry and rate coefficients. It is able to consider all unique adsorption configurations for both adsorbates and saddle points, allowing it to handle high index surfaces and bidentate species. Pynta implements a new saddle point guess generation method called harmonically forced saddle point searching (HFSP). HFSP defines harmonic potentials based on the optimized adsorbate geometries and which bonds are breaking and forming that allow initial placements to be optimized using the GFN1-xTB semiempirical method to create reliable saddle point guesses. This method is reaction class agnostic and fast, allowing Pynta to consider all possible adsorbate site placements efficiently. We demonstrate Pynta on 11 diverse reactions involving monodenate, bidentate, and gas-phase species, many distinct reaction classes, and both a low and a high index facet of Cu. Our results suggest that it is very important to consider reactions between adsorbates adsorbed in all unique configurations for interadsorbate group transfers and reactions on high index surfaces.

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

Extended Lagrangian Born–Oppenheimer molecular dynamics for orbital-free density-functional theory and polarizable charge equilibration models

We report extended Lagrangian Born–Oppenheimer molecular dynamics (XL-BOMD) is formulated for orbital-free Hohenberg–Kohn density-functional theory and for charge equilibration and polarizable force-field models that can be derived from the same orbital-free framework. The purpose is to introduce the most recent features of orbital-based XL-BOMD to molecular dynamics simulations based on charge equilibration and polarizable force-field models. These features include a metric tensor generalization of the extended harmonic potential, preconditioners, and the ability to use only a single Coulomb summation to determine the fully equilibrated charges and the interatomic forces in each time step for the shadow Born–Oppenheimer potential energy surface. The orbital-free formulation has a charge-dependent, short-range energy term that is separate from long-range Coulomb interactions. This enables local parameterizations of the short-range energy term, while the long-range electrostatic interactions can be treated separately. The theory is illustrated for molecular dynamics simulations of an atomistic system described by a charge equilibration model with periodic boundary conditions. The system of linear equations that determines the equilibrated charges and the forces is diagonal, and only a single Ewald summation is needed in each time step. The simulations exhibit the same features in accuracy, convergence, and stability as are expected from orbital-based XL-BOMD.

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

Lattice simulations of inflation

The scalar field theory of cosmological inflation constitutes nowadays one of the preferred scenarios for the physics of the early universe. In this paper we aim at studying the inflationary universe making use of a numerical lattice simulation. Various lattice codes have been written in the last decades and have been extensively used for understating the reheating phase of the universe, but they have never been used to study the inflationary phase itself far from the end of inflation (i.e. about 50 e-folds before the end of inflation). In this paper we use a lattice simulation to reproduce the well-known results of some simple models of single-field inflation, particularly for the scalar field perturbation. The main model that we consider is the standard slow-roll inflation with an harmonic potential for the inflaton field. We explore the technical aspects that need to be accounted for in order to reproduce with precision the nearly scale invariant power spectrum of inflaton perturbations. We also consider the case of a step potential, and show that the simulation is able to correctly reproduce the oscillatory features in the power spectrum of this model. Even if a lattice simulation is not needed in these cases, that are well within the regime of validity of linear perturbation theory, this sets the basis to future work on using lattice simulations to study more complicated models of inflation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The boundary density profile of a Coulomb droplet. Freezing at the edge

In this paper, we revisit the problem of computing the boundary density profile of a droplet of two-dimensional one-component plasma (2D OCP) with logarithmic inter- action between particles in a confining harmonic potential. At a sufficiently low temperature, but still in the liquid phase, the density exhibits oscillations as a function of the distance to the boundary of the droplet. We obtain the density profile numerically using Monte-Carlo simulations of the 2D OCP. We argue that the decay and period of those oscillations can be explained within a picture of the Wigner crystallization near the boundary, where the crystal is gradually melted with the increasing distance to the boundary.

2D OCP↗
DOE OSTI2021

Vibronic and Environmental Effects in Simulations of Optical Spectroscopy

Including both environmental and vibronic effects is important for accurate simulation of optical spectra, but combining these effects remains computationally challenging. We outline two approaches that consider both the explicit atomistic environment and the vibronic transitions. Both phenomena are responsible for spectral shapes in linear spectroscopy and the electronic evolution measured in nonlinear spectroscopy. The first approach utilizes snapshots of chromophore-environment configurations for which chromophore normal modes are determined. We outline various approximations for this static approach that assumes harmonic potentials and ignores dynamic system-environment coupling. The second approach obtains excitation energies for a series of time-correlated snapshots. This dynamic approach relies on the accurate truncation of the cumulant expansion but treats the dynamics of the chromophore and the environment on equal footing. Both approaches show significant potential for making strides toward more accurate optical spectroscopy simulations of complex condensed phase systems.

Chemistry↗
DOE OSTI2021

Equivalence of a harmonic oscillator to a free particle and Eisenhart lift

Highlights: • Equivalence of a harmonic oscillator to a free particle is considered. • The Eisenhart lift is applied to most general harmonic and linear potentials. • In geometric language, equivalence is the result of the conformal flatness of the Eisenhart metric. It is widely known in quantum mechanics that solutions of the Schrödinger equation (SE) for a linear potential are in one-to-one correspondence with the solutions of the free SE. The physical reason for this correspondence is Einstein’s principle of equivalence. What is usually not so widely known is that solutions of the Schrödinger equation with harmonic potential can also be mapped to the solutions of the free Schrödinger equation. The physical understanding of this equivalence is not known as precisely as in the case of the equivalence principle. We present a geometric picture that will link both of the above equivalences with one constraint on the Eisenhart metric.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Nonergodic dynamics in disorder-free potentials

Highlights: • Dynamics in tilted lattices with harmonic confinement is reviewed. • Both spinless and spinful fermions are analyzed. • Local effective tilt is the relevant parameter for nonergodicity. • Neel or domain wall initial states are studied. • Domains with similar spin orientation act as transport and communication barriers. We review the dynamics of interacting particles in disorder-free potentials concentrating on a combination of a harmonic binding with a constant tilt. We show that a simple picture of an effective local tilt describes a variety of cases. Our examples include spinless fermions (as modeled by Heisenberg spin chain in a magnetic field), spinful fermions as well as bosons that enjoy a larger local on-site Hilbert space. We also discuss the domain-wall dynamics that reveals nonergodic features even for a relatively weak tilt as suggested by Doggen et al. (2020). By adding a harmonic potential on top of the static field we confirm that the surprising regular dynamics is not entirely due to Hilbert space shuttering. It seems better explained by the inhibited transport within the domains of identically oriented spins. Once the spin-1/2 restrictions are lifted as, e.g., for bosons, the dynamics involve stronger entanglement generation. Again for domain wall melting, the effect of the harmonic potential is shown to lead mainly to an effective local tilt.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Between Harmonic Crystal and Glass: Solids with Dimpled Potential-Energy Surfaces Having Multiple Local Energy Minima

Solids with dimpled potential-energy surfaces are ubiquitous in nature and, typically, exhibit structural (elastic or phonon) instabilities. Dimpled potentials are not harmonic; thus, the conventional quasiharmonic approximation at finite temperatures fails to describe anharmonic vibrations in such solids. At sufficiently high temperatures, their crystal structure is stabilized by entropy; in this phase, a diffraction pattern of a periodic crystal is combined with vibrational properties of a phonon glass. As temperature is lowered, the solid undergoes a symmetry-breaking transition and transforms into a lower-symmetry phase with lower lattice entropy. Here, we identify specific features in the potential-energy surface that lead to such polymorphic behavior; we establish reliable estimates for the relative energies and temperatures associated with the anharmonic vibrations and the solid–solid symmetry-breaking phase transitions. We show that computational phonon methods can be applied to address anharmonic vibrations in a polymorphic solid at fixed temperature. To illustrate the ubiquity of this class of materials, we present a range of examples (elemental metals, a shape-memory alloy, and a layered charge-density-wave system); we show that our theoretical predictions compare well with known experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Eliminating Imaginary Vibrational Frequencies in Quantum-Chemical Cluster Models of Enzymatic Active Sites

In constructing finite models of enzyme active sites for quantum-chemical calculations, atoms at the periphery of the model must be constrained to stop unphysical rearrangements during geometry relaxation. A simple fixed-atom or “coordinate-lock” approach is commonly employed but leads to undesirable artifacts in the form of small imaginary frequencies. These preclude evaluation of finite-temperature free-energy corrections, limiting thermochemical calculations to enthalpies only. Full-dimensional vibrational frequency calculations are possible by replacing the fixed-atom constraints with harmonic confining potentials. Here, we compare that approach to an alternative strategy in which fixed-atom contributions to the Hessian are simply omitted. While the latter strategy does eliminate imaginary frequencies, it tends to underestimate both the zero-point energy and the vibrational entropy while introducing artificial rigidity. Harmonic confining potentials eliminate imaginary frequencies and provide a flexible means to construct active-site models that can be used in unconstrained geometry relaxations, affording better convergence of reaction energies and barrier heights with respect to the model size, as compared to models with fixed-atom constraints.

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

Motional Squeezing for Trapped Ion Transport and Separation

Transport, separation, and merging of trapped ion crystals are essential operations for most large-scale quantum computing architectures. In this Letter, we develop a theoretical framework that describes the dynamics of ions in time-varying potentials with a motional squeeze operator, followed by a motional displacement operator. Using this framework, we develop a new, general protocol for trapped ion transport, separation, and merging. We show that motional squeezing can prepare an ion wave packet to enable transfer from the ground state of one trapping potential to another. Here, the framework and protocol are applicable if the potential is harmonic over the extent of the ion wave packets at all times. As illustrations, we discuss two specific operations: changing the strength of the confining potential for a single ion and separating same-species ions with their mutual Coulomb force. Both of these operations are, ideally, free of residual motional excitation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Reverse Polarizability of Rare Earth Ions (La 3+ , Gd 3+ , Lu 3+ , Y 3+ ) in Tellurite Glasses and Glass Ceramics for Optical Limiting

All-optical modulation using inherent third-order optical nonlinearity of a medium has garnered considerable interest in photonics and optoelectronics. Herein, nonlinear optical (NLO) properties of tellurite glasses and glass ceramics (GCs) containing four different rare earths (RE = La, Gd, Lu, and Y) have been deliberated in near-infrared regions under an ultrafast regime. The La-based glass exhibits ~10 times higher nonlinear refraction (n 2 ) and absorption (α 2 ) than reported NLO materials. The NLO susceptibility [χ (3) ] trend in the studied glasses is La > Gd > Lu > Y, matching with RE 3+ polarizability. Furthermore, Ln 2 Te 6 O 15 nanocrystallite-embedded transparent GCs exhibit a larger NLO coefficient due to the enhanced local field from oxygen vacancies in crystallites. Interestingly, the trend of χ (3) in GCs follows the sequence of Y > Lu > Gd > La, precisely opposite to the glasses. This observation challenges the general polarizability approach of RE 3+ ions, emphasizing that quadratic hyperpolarizability of RE 3+ is pivotal for NLO properties of GCs. Among the studied matrices, Y-containing GCs showed the lowest optical limiting (OL) threshold (5.4 mJ/cm 2 at 800 nm), much lower than those of the reported NLO materials, suggesting its potential as a femtosecond NIR-laser safety material. A combination of large α 2 and n 2 from the studied matrices indicates their advantage for harmonic generation, potentially aiding in the design of ultrafast signal processing devices.

36 MATERIALS SCIENCE↗