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Results for “zero point energy”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

We introduce a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing . The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we establish a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work indicate a more efficient scaling of computational cost with molecular size as compared to other methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Is zero-point energy physical? A toy model for Casimir-like effect

Zero-point energy is generally known to be unphysical. Casimir effect, however, is often presented as a counterexample, giving rise to a conceptual confusion. To resolve the confusion we study foundational aspects of Casimir effect at a qualitative level, but also at a quantitative level within a simple toy model with only 3 degrees of freedom. In particular, we point out that Casimir vacuum is not a state without photons, and not a ground state for a Hamiltonian that can describe Casimir force. Instead, Casimir vacuum can be related to the photon vacuum by a non-trivial Bogoliubov transformation, and it is a ground state only for an effective Hamiltonian describing Casimir plates at a fixed distance. At the fundamental microscopic level, Casimir force is best viewed as a manifestation of van der Waals forces. - Highlights: • A toy model for Casimir-like effect with only 3 degrees of freedom is constructed. • Casimir vacuum can be related to the photon vacuum by a non-trivial Bogoliubov transformation. • Casimir vacuum is a ground state only for an effective Hamiltonian describing Casimir plates at a fixed distance. • At the fundamental microscopic level, Casimir force is best viewed as a manifestation of van der Waals forces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

Uncertainty relations, zero point energy and the linear canonical group

The close relationship between the zero point energy, the uncertainty relations, coherent states, squeezed states, and correlated states for one mode is investigated. This group-theoretic perspective enables the parametrization and identification of their multimode generalization. In particular the generalized Schroedinger-Robertson uncertainty relations are analyzed. An elementary method of determining the canonical structure of the generalized correlated states is presented.

Sudarshan, E. C. G.↗
DOE OSTI2019

Trajectory-adjusted electronic zero point energy in classical Meyer-Miller vibronic dynamics: Symmetrical quasiclassical application to photodissociation

An electronic zero-point energy (ZPE) adjustment protocol is proposed within the context of the symmetrical quasiclassical (SQC) quantization of the electronic oscillator degrees of freedom (DOF) in classical Meyer-Miller (MM) vibronic dynamics for the molecular dynamics treatment of electronically nonadiabatic processes. The “adjustment” procedure maintains the same initial and final distributions of coordinates and momenta in the electronic oscillator DOF as previously given by the SQC windowing protocol but modifies the ZPE parameter in the MM Hamiltonian, on a per trajectory basis, so that the initial nuclear forces are precisely those corresponding to the initial electronic quantum state. Examples demonstrate that this slight modification to the standard SQC/MM approach greatly improves treatment of the multistate nonadiabatic dynamics following a Franck-Condon type vertical excitation onto a highly repulsive potential energy surface as is typical in the photodissociation context.

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

Extended Hamiltonian molecular dynamics: semiclassical trajectories with improved maintenance of zero point energy

It is well known that classical trajectories, even if they are initiated with zero point energy (ZPE) in each mode (trajectories initiated this way are commonly called quasiclassical trajectories), do not maintain ZPE in the final states. The energy of high-frequency modes will typically leak into low-frequency modes or relative translation of subsystems during the time evolution. This can lead to severe problems such as unphysical dissociation of a molecule, production of energetically disallowed reaction products, and unphysical product energy distributions. Here a new molecular dynamics method called extended Hamiltonian molecular dynamics (EHMD) is developed to improve the ZPE problem in classical molecular dynamics. In EHMD, two images of a trajectory are connected by one or more springs. The EHMD method is tested with the Henon–Heiles Hamiltonian in reduced and real units and with a Hamiltonian with quartic anharmonicity in real units, and the method is found to improve zero-point maintenance as intended.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1978

On the contribution of intramolecular zero point energy to the equation of state of solid H2

Experimental evidence shows that the internal zero-point energy of the H2 molecule exhibits a relatively strong pressure dependence in the solid as well as changing considerably upon condensation. It is shown that these effects contribute about 6% to the total sublimation energy and to the pressure in the solid state. Methods to modify the ab initio isolated pair potential to account for these environmental effects are discussed.

Chandrasekharan, V.↗
DOE OSTI2019

Vibrational modes and quantum zero-point energy of hydrogen in ZrH 0.0155 and ZrH 2

We report on an inelastic neutron scattering study of the proton dynamics in ZrH 0.0155 and ε-ZrH 2 . In particular, we present measurements of the incoherent dynamic structure factor, generalized vibrational density of states, and proton momentum distribution of these two materials. Our results are generally consistent with theoretical predictions of Elsässer et al. [Mat. Res. Soc. Symp. Proc. 453 221–226 (1997)]. They argued that the effective Born-Oppenheimer potential experienced by the hydrogen atoms in ε-ZrH 2 is nearly isotropic and harmonic at energies below 0.3 eV, but becomes anisotropic and anharmonic for higher energies. At low temperatures, the proton momentum distribution is dominated by the quantum-mechanical ground state of the protons. We find that it assumes a Gaussian shape, consistent with the concept that the potential surface is approximately harmonic for small displacements of the hydrogen atoms. However, the anharmonicity of the potential becomes readily apparent in the excited states of the hydrogen atoms, as the harmonic approximation breaks down in the description of the multiphonon bands.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy

The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one- and three-dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. Here, we consider three flavors of mixed quantum-classical dynamics: (i) the classical path approximation (CPA), (ii) Ehrenfest dynamics, and (iii) symmetrical quasiclassical (SQC) dynamics. Our findings are as follows: (i) The CPA fails to recover a consistent description of spontaneous emission, (ii) a consistent “spontaneous” emission can be obtained from Ehrenfest dynamics, provided that one starts in an electronic superposition state, and (iii) spontaneous emission is always obtained using SQC dynamics. Using the SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by Miller [J. Chem. Phys. 69, 2188 (1978)] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights interesting possibilities for studying light-matter interactions with semiclassical mechanics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Topological and magnetic properties of a noncollinear spin state on a honeycomb lattice in a magnetic field

Here, this paper studies the topological and magnetic properties of a noncollinear spin state on a honeycomb lattice that evolves from coplanar to ferromagnetic with a magnetic field applied along the z axis. The coplanar state is stabilized by nearest-neighbor ferromagnetic interactions, single-ion anisotropy along z, and DzyaloshinskiiMoriya interactions between next-nearest-neighbor sites. Below the critical field H$_c$ that aligns the spins, the magnetic unit cell contains six sites and the spin dynamics contains six magnon modes. Although the classical energy is degenerate with respect to the twist angle φ between nearest-neighbor spins, the dependence of the free energy on φ at low temperatures is dominated by the magnon zero-point energy, which contains extremum at φ = πl/3 for integer l. The only unique ground states GS(φ) have l = 0 or 1. For H < H$'_c$, the zero-point energy has minima at even l and the ground state is GS(0); for H$'_c$ < H < H$'_c$, the zero-point energy has minima at odd l and the ground state is GS(π/3). In GS(0), the magnon density of states exhibits five distinct topological phases with increasing field associated with the opening and closing of energy gaps between two or three magnonic bands. While the Berry curvature vanishes for the coplanar φ = 0 phase in zero field, the Berry curvature and Chern numbers exhibit signatures of the five topological phases below H$'_c$. Whereas the Berry curvature and Chern number are sensitive to changes in the magnon density of states within GS(π/3), the inelastic spectrum S(k,ω) is sensitive to changes in the intensity of the magnon modes in the different magnetic phases GS(0) and GS(π/3) rather than the five topological phases within GS(π/3).

Fishman, Randy S. [Oak Ridge National Laboratory (↗
DOE OSTI2018

Assessing the Predictive Power of Density Functional Theory in Finite-Temperature Hydrogen Adsorption/Desorption Thermodynamics

Density functional theory (DFT) has been widely employed to study the gas adsorption properties of surface-based or nanoscale structures. However, recent indications raise questions about the trustworthiness of some literature values, especially in terms of the DFT exchange–correlation (XC) functional. Using hydrogen adsorption on metalloporphyrin-incorporated graphenes (MPIGs) as an example, we diagnosed the trustworthiness of DFT results, meaning the range of expected variations in the DFT prediction of experimentally measurable quantities, in characterizing the gas adsorption/desorption thermodynamics. DFT results were compared in terms of XC functionals and vibrational effects that have been overlooked in the community. We decomposed free energy associated with gas adsorption into constituting components (binding energy, zero-point energy, and vibrational free energy) to systematically analyze the origin of deviations associated with the most commonly adopted DFT functionals in the field. We then quantify the deviations in the measurable quantities, such as operating temperature or pressure for hydrogen adsorption/desorption depending on the level of approximations. In conclusion, using chemical potential change associated with gas adsorption as a descriptor, we identify the required calculational accuracy of DFT to predict the room-temperature hydrogen storage material.

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

Quantum Sieving for Isotopic Separations of Gases Using Porous Materials─30 Years of Progress

Here, this paper reviews theoretical and experimental efforts to establish microporous materials that can be used to separate isotopologues of molecular gases such as H 2 and D 2 . Emphasis is placed on use of simplified models to highlight the quantum phenomena that make these separations possible. In equilibrium adsorption, differences in zero point energy in the adsorbed states of molecules favor binding of heaver isotopologues (e.g. D 2 relative to H 2 ). Experimental data showing this effect was reported as early as 1933, but the theoretical work of Beenakkers et al. in 1995 [Chem. Phys. Lett. 232 (1995) 379-382] spurred modern efforts to develop materials with strong so-called quantum sieving. In porous materials where the transition state for molecular diffusion is more strongly confined than the energy minima associated with equilibrium adsorption, differences in zero point energies between these two sites can lead to isotopic differences in molecular diffusivities. This effect favors diffusion of heavier species (e.g. D 2 ) relative to lighter species (e.g. H 2 ). This so-called kinetic quantum sieving has been observed experimentally in porous carbons and in porous organic cage materials. We show that quantum tunneling, which favors hopping of lighter species across energy barriers, diminishes the strength of kinetic quantum sieving but that it appears to make only a small contribution to the net molecular diffusivities in many porous materials of practical interest.

Sholl, David S. [Oak Ridge National Laboratory (OR↗
DOE OSTI2018

Properties of Feshbach and “shape”-resonances in ozone and their role in recombination reactions and anomalous isotope effects

Computational modelling of recombination reactions that form ozone require the inclusion of several quantum mechanical effects such as symmetry, zero-point energy, scattering resonances and tunneling. Major elements of theory for rigorous description of this process are reviewed, with emphasis on interpreting the famous anomalous isotope effect due to substitutions of 18 O. In this work, three reaction pathways, for the formation of symmetric and asymmetric isotopologues of ozone, are introduced and a hierarchy of theory levels is outlined. Lower levels of theory are used to account for the effects of symmetry, isotope mass, rotational excitations and vibrational zero-point energy differences. They happen to be equivalent to statistical descriptions of the process and do not show anomalous isotope effects. Properties of scattering resonances should be included at the next level of theory, and may finally explain the isotope effect. Shape resonances, trapped behind the centrifugal barrier and populated by tunneling, can be studied by neglecting couplings between the diabatic ro-vibrational states of the system. Inclusion of these couplings enables the formation of Feshbach resonances. Accurate calculations using hyper-spherical coordinates are performed to obtain resonance energies, lifetimes and wavefunctions. Differences between the shape resonances and Feshbach resonances are emphasized.

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

Sensitivity of the Shock Initiation Threshold of 1,3,5-Triamino-2,4,6-trinitrobenzene (TATB) to Nuclear Quantum Effects

Approximating the dynamics of atomic nuclei with classical equations of motion in molecular dynamics (MD) simulations causes an overprediction of the specific heat and omits zero-point energy which can have a crucial effect on predictions of the response of materials under dynamical loading. We use quantum and classical thermostats in reactive MD simulations to characterize the effect of energy distribution on the initiation and decomposition of the explosive 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) under shock and thermal loading. Shock simulations using the multiscale shock technique (MSST) show that nuclear quantum effects not only increase the temperature rise during dynamical loading but also lower the shock temperature corresponding to the threshold for initiation of chemical reactions. The lower specific heat and presence of zero point energy contribute approximately equally to these effects. Thermal decomposition simulations show that nuclear quantum effects lower the activation barrier associated with reaction compared to classical simulations. Here, comparing quantum and classical simulations as a function of average kinetic energy shows that classical baths result in faster kinetics as compared with quantum ones; we explore the molecular origins of this observation.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions

This work examines the viability of matrix completion methods as cost-effective alternatives to full nuclear Hessians for calculating quantum and variational effects in chemical reactions. The harmonic variety-based matrix completion (HVMC) algorithm, developed in a previous study (https://doi.org/10.1063/5.0018326), exploits the low-rank character of the polynomial expansion of potential energy to recover, using a small sample, vibrational frequencies (square roots of nuclear Hessian eigenvalues) constituting the reaction path. Furthermore, these frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performance is examined for four SN2 reactions and five hydrogen transfer reactions, with each H-transfer reaction consisting of at least one vibrational mode strongly coupled to the reaction coordinate. HVMC is robust and captures zero-point energies, vibrational free energies, zero-curvature tunneling, and adiabatic ground state and free energy barriers as well as their positions on the reaction coordinate. For medium to large reactions involving H-transfer, with the exception of the most complex Ir catalysis system, less than 35% of total eigenvalue information is necessary for accurate recovery of key VTST-MT observables.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1999

The Atomization Energy of Mg4

The atomization energy of Mg4 is determined using the MP2 and CCSD(T) levels of theory. Basis set incompleteness, basis set extrapolation, and core-valence effects are discussed. Our best atomization energy, including the zero-point energy and scalar relativistic effects, is 24.6+/-1.6 kcal per mol. Our computed and extrapolated values are compared with previous results, where it is observed that our extrapolated MP2 value is good agreement with the MP2-R12 value. The CCSD(T) and MP2 core effects are found to have the opposite signs.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1998

C2 Fragmentation Energy of C60 Revisited: Theory Disagrees with Most Experiments

Following our earlier work on the subject, we have carried out density functional theory (DFT) and second-order Moller-Plesset perturbation theory (MP2) calculations of the dissociation energy of the reaction C60 yields C58 + C2 using polarized basis sets and geometries optimized with DFT methods. The present theoretical results support an electronic fragmentation energy D(sub e) around 10-11 eV in disagreement with most experimental results that place the dissociation energy D(sub o) (including zero point energy) around 7-8 eV. The plausible errors remaining in the theoretical calculations are unlikely to account for this big difference (2-4 eV).

Boese, A. Daniel↗
DOE OSTI2024

High-resolution infrared spectroscopy of jet cooled cyclobutyl in the α-CH stretch region: large-amplitude puckering dynamics in a 4-membered ring radical

We report gas-phase cyclobutyl radical (c-C 4 H 7 ) is generated at a rotational temperature of T rot = 26(1) K in a slit-jet discharge mixture of 70% Ne/30% He and 0.5–0.6% cyclobromobutane (c-C 4 H 7 Br). A fully rovibrationally resolved absorption spectrum of the α-CH stretch fundamental band between 3062.9 cm −1 to 3075.7 cm −1 is obtained and analyzed, yielding first precision structural and dynamical information for this novel radical species. The α-CH stretch band origin is determined to be 3068.7887(4) cm −1 , which implies only a modest (≈0.8 cm −1 ) blue shift from rotationally unresolved infrared spectroscopic studies of cyclobutyl radicals in liquid He droplets [ A. R. Brown, P. R. Franke and G. E. Douberly, J. Phys. Chem. A , 2017, 121 , 7576–7587]. Of particular dynamical interest, a one-dimensional potential energy surface with respect to the ring puckering coordinate is computed at CCSD(T)/ANO2 level of theory and reveals a double minimum C s puckered geometry, separated by an exceedingly shallow planar C 2v transition state barrier (E barr ≈ 1 cm −1 ). Numerical solutions on this double minimum potential yield a zero-point energy for the ground state (E zero-point ≈ 27 cm −1 ) greatly in excess of the interconversion barrier. This is indicative of highly delocalized, large amplitude motion of the four-membered ring structure, for which proper vibrationally averaging of the moment of inertia tensor reproduces the experimentally determined inertial defect remarkably well. Finally, intensity alternation in the experimental spectrum due to nuclear spin statistics upon exchange of three indistinguishable H atom pairs (IH = ½) matches K a + K c = even : odd = 36 : 28 predictions, implying that the unpaired electron in the radical center lies in an out-of-plane p π orbital. Thus, high-resolution infrared spectroscopy provides first experimental confirmation of a shallow double minimum ring puckering potential with a highly delocalized ground state wave function peaked at a planar C 2v transition state geometry consistent with a cyclobutyl π radical.

Chemistry↗