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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Fractional occupation numbers and self-interaction correction-scaling methods with the Fermi-Löwdin orbital self-interaction correction approach

In this work, we present a new assessment of the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) approach with an emphasis on its performance for predicting energies as a function of fractional occupation numbers (FONs) for various multielectron systems. Our approach is implemented in the massively parallelized NWChem quantum chemistry software package and has been benchmarked on the prediction of total energies, atomization energies, and ionization potentials of small molecules and relatively large aromatic systems. Within our study, we also derive an alternate expression for the FLO-SIC energy gradient expressed in terms of gradients of the Fermi-orbital eigenvalues and revisit how the FLO-SIC methodology can be seen as a constrained unitary transformation of the canonical Kohn–Sham orbitals. Finally, we conclude with calculations of energies as a function of FONs using various SIC-scaling methods to test the limits of the FLO-SIC formalism on a variety of multielectron systems. We find that these relatively simple scaling methods do improve the prediction of total energies of atomic systems as well as enhance the accuracy of energies as a function of FONs for other multielectron chemical species.

fractional occupation number↗
DOE OSTI2018

Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number

Approximate functionals used in practical density functional theory (DFT) deviate from the piecewise linear behavior of the exact functional for fractional charges. This deviation causes excess charge delocalization, which leads to incorrect densities, molecular properties, barrier heights, band gaps, and excitation energies. Here, we present a simple delocalization function for characterizing this error and find it to be almost perfectly linear vs the fractional electron number for systems spanning in size from the H atom to the C 12 H 14 polyene. This causes the delocalization energy error to be a quadratic polynomial in the fractional electron number, which permits us to assess the comparative performance of 47 popular and recent functionals through the curvature. The quadratic form further suggests that information about a single fractional charge is sufficient to eliminate the principal source of delocalization error. Generalizing traditional two-point information like ionization potentials or electron affinities to account for a third, fractional charge-based data point could therefore permit fitting/tuning of functionals with lower delocalization error.

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

Single classical field description of interacting scalar fields

In this report we test the degree to which interacting Bosonic systems can be approximated by a classical field as total occupation number is increased. This is done with our publicly available code repository, QIBS, a new massively parallel solver for these systems. We use a number of toy models well studied in the literature and track when the classical field description admits quantum corrections, called the quantum breaktime. This allows us to test claims in the literature regarding the rate of convergence of these systems to the classical evolution. We test a number of initial conditions, including coherent states, number eigenstates, and field number states. We find that of these initial conditions, only number eigenstates do not converge to the classical evolution as occupation number is increased. We find that systems most similar to scalar field dark matter exhibit a logarithmic enhancement in the quantum breaktime with total occupation number. Systems with contact interactions or with field number state initial conditions, and linear dispersions, exhibit a power law enhancement. Finally, we find that the breaktime scaling depends on both model interactions and initial conditions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Interferometer response to geontropic fluctuations

We model vacuum fluctuations in quantum gravity with a scalar field, characterized by a high occupation number, coupled to the metric. The occupation number of the scalar is given by a thermal density matrix, whose form is motivated by fluctuations in the vacuum energy, which have been shown to be conformal near a light-sheet horizon. For the experimental measurement of interest in an interferometer, the size of the energy fluctuations is fixed by the area of a surface bounding the volume of spacetime being interrogated by an interferometer. We compute the interferometer response to these “geontropic” scalar-metric fluctuations, and apply our results to current and future interferometer measurements, such as LIGO and the proposed GQuEST experiment.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Linear scaling pseudo Fermi-operator expansion for fractional occupation

Recursive Fermi-operator expansion methods for the calculation of the idempotent density matrix are valid only at zero electronic temperature with integer occupation numbers. We show how such methods can be modified to include fractional occupation numbers of an approximate or pseudo Fermi-Dirac distribution and how the corresponding entropy term of the free energy is calculated. The proposed methodology is demonstrated and evaluated for different electronic structure methods including density functional tight-binding theory, Kohn-Sham density functional theory using numerical orbitals, and quantum chemistry Hartree-Fock theory using Gaussian basis functions.

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

A Chain Model of a Zigzag Contact of Lateral Graphene-Like Heterostructures

A simple structural model is proposed for the zigzag interface formed by contacting two-dimensional graphene-like compounds AB and CD (both free and formed on a metal). For the graphene–hexagonal boron nitride system, analytical expressions for the electron spectrum, density of states, and atom occupation numbers at the interface are obtained. The results of calculating the densities of states and occupation numbers within two alternative approximations are in good agreement.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Mixed quantum–classical approach to model non-adiabatic electron–nuclear dynamics: Detailed balance and improved surface hopping method

We develop a density matrix formalism to describe coupled electron–nuclear dynamics. To this end, we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a classical trajectory of the nuclei. Using this Hamiltonian, we derive equations of motion for the electronic occupation numbers and for the nuclear coordinates and momenta. We show that, in the limit, when the number of nuclear degrees of freedom coupled to a given electronic transition is sufficiently high (i.e., the strong decoherence limit), the equations of motion for the electronic occupation numbers become Markovian. Furthermore, the transition rates in these (rate) equations are asymmetric with respect to the lower-to-higher energy transitions and vice versa. In thermal equilibrium, such asymmetry corresponds to the detailed balance condition. We also study the equations for the electronic occupations in the non-Markovian regime and develop a surface hopping algorithm based on our formalism. To treat the decoherence effects, we introduce additional “virtual” nuclear wave packets whose interference with the “real” (physical) wave packets leads to the reduction in coupling between the electronic states (i.e., decoherence) as well as to the phase shifts that improve the accuracy of the numerical approach. Remarkably, the same phase shifts lead to the detailed balance condition in the strong decoherence limit.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

A complete quasiclassical map for the dynamics of interacting fermions

We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving Heisenberg's equation of motion for one-body operators. In order to accommodate the effect of two-body terms, we further impose quantization on the spin-dependent occupation numbers in the classical equations of motion, with a parameter that is determined self-consistently. Expectation values for observables are taken with respect to an initial quasiclassical distribution that respects the original quantization of the occupation numbers. The proposed classical map becomes complete under the evolution of quadratic Hamiltonians and is extended for all even order observables. We show that the map provides an accurate description of the dynamics for an interacting quantum impurity model in the coulomb blockade regime, at both low and high temperatures. In conclusion, the numerical results are aided by a novel importance sampling scheme that employs a reference system to reduce significantly the sampling effort required to converge the classical calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Graph-based quantum response theory and shadow Born–Oppenheimer molecular dynamics

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born–Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. Further, the proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Quasi-Fermi liquid behavior in a one-dimensional system of interacting spinless fermions

We present numerical evidence for a paradigm in one-dimensional interacting fermion systems, whose phenomenology has traits of both Luttinger liquids and Fermi liquids. This state, dubbed a quasi-Fermi liquid, possesses a discontinuity in its fermion occupation number at the Fermi momentum. The excitation spectrum presents particlelike quasiparticles and absence of holelike quasiparticles, giving rise instead to edge singularities. Such a state is realized in a one-dimensional spinless fermion lattice Hamiltonian by fine-tuning the interactions to a regime where they become irrelevant in the renormalization group sense. We show, using uniform infinite matrix products states and finite-entanglement scaling analysis, that the system ground state is characterized by a Luttinger parameter K = 1 and a discontinuous jump in the fermion occupation number. We support the characterization with calculations of the spectral function that show a particle-hole asymmetry reflected in the existence of well-defined Landau quasiparticles above the Fermi level and edge singularities without the associated quasiparticles below. Furthermore, these results indicate that the quasi-Fermi liquid paradigm can be realized beyond the low-energy perturbative realm.

1-dimensional systems↗
DOE OSTI2022

Provably accurate simulation of gauge theories and bosonic systems

Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions, and also to both abelian and non-abelian gauge theories. We show that if states in these models are truncated by imposing an upper limit Λ on each local quantum number, and if the initial state has low local quantum numbers, then an error at most ϵ can be achieved by choosing Λ to scale polylogarithmically with ϵ − 1 , an exponential improvement over previous bounds based on energy conservation. For the Hubbard-Holstein model, we numerically compute a bound on Λ that achieves accuracy ϵ , obtaining significantly improved estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes; the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our result on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with accuracy ϵ by truncating local quantum numbers at Λ = polylog ( ϵ − 1 ) .

Tong, Yu↗
DOE OSTI2023

PANDEMIC: Occupancy driven predictive ventilation control to minimize energy consumption and infection risk

During the SARS-CoV-2 (COVID-19) pandemic, governments around the world have formulated policies requiring ventilation systems to operate at a higher outdoor fresh air flow rate for a sufficient time, which has led to a sharp increase in building energy consumption. Therefore, it is necessary to identify an energy-efficient ventilation strategy to reduce the risk of infection. In this study, we developed an occupant-number-based model predictive control (OBMPC) algorithm for building ventilation systems. First, we collected the occupancy and Heating, ventilation, and air conditioning system (HVAC) data from March to July 2021. Then, four different models (Auto regression moving average-based multilayer perceptron (ARMA_MLP), Recurrent neural networks (RNN), Long short-term memory networks (LSTM), and Nonhomogeneous Markov with change points detection (NH_Markov)) were used to predict the number of room occupants from 15 min to 24 h ahead with an interval output. We found that each model could predict the number of occupants with 85% accuracy using a one-person offset. Furthermore, the accuracy of 15 min of the ahead prediction could reach 95% with a one-person offset, but none of them could track abrupt changes. The occupancy prediction results were used to calculate the ventilation demand using the Wells-Riley equation, and the upper bound can maintain an infection risk lower than 2% for 93% of the day. This OBMPC model could reduce the coil load by 52.44% and shift the peak load by 3 h up to 5 kW compared with 24 × 7 h full outdoor air (OA) system when people wear masks in the space. The occupancy prediction uncertainty could cause a 9% to 26% difference in demand ventilation, a 0.3°C to 2.4°C difference in zone temperature, a 28.5% to 44.5% difference in outdoor airflow rate, and a 10.7% to 28.2% difference in coil load.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2018

Work drives time evolution

We propose the idea that time evolution of quantum systems is driven by work. The formalism presented here falls within the scope of a recently proposed theory of gravitating quantum matter where extractible work, and not energy, is responsible for gravitation. Our main assumption is that extractible work, and not the Hamiltonian, dictates dynamics. We find that expectation values of meaningful quantities, such as the occupation number, deviate from those predicted by standard quantum mechanics. The scope, applications and validity of this proposal are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Underlying simplicity of 5f unoccupied electronic structure

Using a simple empirical model based upon the bremsstrahlung isochromat spectroscopy of elemental Th, it is possible to explain the recent high energy resolution fluorescence detection measurements of UF 4 (n = 2) and UCd 11 (n = 3) as well as the new inverse photoelectron spectroscopy of Pu 2 O 3 (n = 5), where n is the 5f occupation number. Furthermore, a critical issue in this analysis is the assumption that the Th 5f states are essentially empty, which will be confirmed both experimentally and computationally. Thus, for 5f systems, this simple model provides a unified and consistent picture of 5f unoccupied density of states in simple, localized systems, as the 5f occupation varies in the early part of the series, for n = 0, 2, 3, and 5.

36 MATERIALS SCIENCE↗
DOE OSTI2024

The accuracies of effective interactions in downfolding coupled-cluster approaches for small-dimensionality active spaces

Here, this paper evaluates the accuracy of the Hermitian form of the downfolding procedure using the double unitary coupled cluster (DUCC) ansatz on the benchmark systems of linear chains of hydrogen atoms, H6 and H8. The computational infrastructure employs the occupation-number-representation codes to construct the matrix representation of arbitrary second-quantized operators, allowing for the exact representation of exponentials of various operators. The tests demonstrate that external amplitudes from standard single-reference coupled cluster methods that sufficiently describe external (out-of-active-space) correlations reliably parameterize the Hermitian downfolded effective Hamiltonians in the DUCC formalism. The results show that this approach can overcome the problems associated with losing the variational character of corresponding energies in the corresponding SR-CC theories.

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

Occupation probabilities as variables in electronic structure theory: cooper pairing, OP-NSOFT-Cs,t, and the homogeneous electron liquid

The energy functional of a novel electronic structure theory, OP-NSOFT, has as variables the natural spin orbitals (NSO) of the trial function and their joint occupation probabilities in the search for the ground state energy. When occupancy is restricted to the spin-paired NSOs of DOCI, the resulting theory, OP-NSOFT-0, scales as M 3 , with M the size of the one-electron basis set. Accurate results were obtained for small molecules, particularly near dissociation where single reference theories like DFT are inaccurate. The homogeneous electron liquid (HEL) could serve as a test bed of OP-NSOFT for condensed systems, but OP-NSOFT-0 reduces to the Hartree–Fock approximation for the HEL. Cooper pairing is introduced instead, both singlet pairing, OP-NOFT-Cs, and fully polarized triplet pairing, OP-NSOFT-Ct. The former yields 1/3 of the diffusion-Monte-Carlo correlation energy, the latter 1/2 to 1/3 with decreasing electron density for r s values between 1 and 10. Both yield the discontinuity in the single-particle occupation number required by the Luttinger theorem. Furthermore, two-state joint occupation probabilities illustrate the importance of electron–electron small-angle scattering in establishing electron correlation in the unpolarized HEL.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Reduced-Cost Four-Component Relativistic Double Ionization Potential Equation-of-Motion Coupled-Cluster Approaches with 4-Hole–2-Particle Excitations and Three-Body Clusters

The double ionization potential (DIP) equation-ofmotion (EOM) coupled-cluster (CC) method with 4-hole−2- particle (4h-2p) excitations on top of the CC with singles, doubles, and triples calculation, abbreviated as DIP-EOMCCSDT(4h-2p), along with its perturbative DIP-EOMCCSD(T)(a)(4h-2p) approximation, are extended to a relativistic four-component (4c) framework. In addition, we introduce and test a new computationally practical DIP-EOMCC approach, which we call DIPEOMCCSD( T)(ã)(4h-2p), that approximates the treatment of 4h- 2p correlations within the DIP-EOMCCSD(T)(a)(4h-2p) method and reduces the $\mathcal{N}$ 8 scaling characterizing DIP-EOMCCSDT(4h- 2p) and DIP-EOMCCSD(T)(a)(4h-2p) to $\mathcal{N}$ 7 with the system size $\mathcal{N}$. Further improvements in computational efficiency are obtained using the frozen natural spinor (FNS) approximation to reduce the numbers of unoccupied spinors entering the correlated steps of the DIP-EOMCC calculations according to a well-defined occupation-number-based threshold. The resulting 4c-FNS-DIPEOMCC approaches are used to compute DIPs for the series of inert gas atoms from argon to radon as well as the vertical DIPs in Cl 2 , Br 2 , HBr, and HI, which have been experimentally examined in the past. We demonstrate that, when using complete basis set extrapolations and FNS truncation threshold of 10 −4.5 , the 4c-FNS-DIP-EOMCCSD(T)(ã)(4h-2p) calculations are capable of predicting DIPs in agreement with experimental data, improving upon their nonrelativistic and spin-free scalar-relativistic counterparts, particularly when examining DIPs characterized by stronger spin−orbit coupling effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗