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DOE OSTI2014

Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study

We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix yields the energy density and orbital occupation energies. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single particle energy spectrum obeying a total energy sum rule. For mean-field systems the energy density matrix recovers the exact spectrum. When correlation becomes important, the occupation energies resemble quasiparticle energies in some respects. We explore the occupation energy spectrum for the finite 3D homogeneous electron gas in the metallic regime and an isolated oxygen atom with ground state quantum Monte Carlo techniques imple- mented in the QMCPACK simulation code. The occupation energy spectrum for the homogeneous electron gas can be described by an effective mass below the Fermi level. Above the Fermi level evanescent behavior in the occupation energies is observed in similar fashion to the occupation numbers of the 1RDM. A direct comparison with total energy differences demonstrates a quantita- tive connection between the occupation energies and electron addition and removal energies for the electron gas. For the oxygen atom, the association between the ground state occupation energies and particle addition and removal energies becomes only qualitative. The energy density matrix provides a new avenue for describing energetics with quantum Monte Carlo methods which have traditionally been limited to total energies.

density matrix↗

DOE OSTI2016

Inter-ribbon tunneling in graphene: An atomistic Bardeen approach

A weakly coupled system of two crossed graphene nanoribbons exhibits direct tunneling due to the overlap of the wavefunctions of both ribbons. We apply the Bardeen transfer Hamiltonian formalism, using atomistic band structure calculations to account for the effect of the atomic structure on the tunneling process. The strong quantum-size confinement of the nanoribbons is mirrored by the one-dimensional character of the electronic structure, resulting in properties that differ significantly from the case of inter-layer tunneling, where tunneling occurs between bulk two-dimensional graphene sheets. The current-voltage characteristics of the inter-ribbon tunneling structures exhibit resonance, as well as stepwise increases in current. Both features are caused by the energetic alignment of one-dimensional peaks in the density-of-states of the ribbons. Resonant tunneling occurs if the sign of the curvature of the coupled energy bands is equal, whereas a step-like increase in the current occurs if the signs are opposite. Changing the doping modulates the onset-voltage of the effects as well as their magnitude. Doping through electrostatic gating makes these structures promising for application towards steep slope switching devices. Using the atomistic empirical pseudopotentials based Bardeen transfer Hamiltonian method, inter-ribbon tunneling can be studied for the whole range of two-dimensional materials, such as transition metal dichalcogenides. The effects of resonance and of step-like increases in the current we observe in graphene ribbons are also expected in ribbons made from these alternative two-dimensional materials, because these effects are manifestations of the one-dimensional character of the density-of-states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Resonant particle production during inflation: a full analytical study

We revisit the study of the phenomenology associated to a burst of particle production of a field whose mass is controlled by the inflaton field and vanishes at one given instance during inflation. This generates a bump in the correlators of the primordial scalar curvature. We provide a unified formalism to compute various effects that have been obtained in the literature and confirm that the dominant effects are due to the rescattering of the produced particles on the inflaton condensate. We improve over existing results (based on numerical fits) by providing exact analytic expressions for the shape and height of the bump, both in the power spectrum and the equilateral bispectrum. We then study the regime of validity of the perturbative computations of this signature. Finally, we extend these computations to the case of a burst of particle production in a sector coupled only gravitationally to the inflaton.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

Algebraic structure of general electromagnetic fields and energy flow

Highlights: > Algebraic structure of general electromagnetic fields in stationary spacetime. > Eigenvalues and eigenvectors of the electomagnetic field tensor. > Energy-momentum in terms of eigenvectors and Killing vector. > Explicit form of reference frame with vanishing Poynting vector. > Application of formalism to Bessel beams. - Abstract: The algebraic structures of a general electromagnetic field and its energy-momentum tensor in a stationary space-time are analyzed. The explicit form of the reference frame in which the energy of the field appears at rest is obtained in terms of the eigenvectors of the electromagnetic tensor and the existing Killing vector. The case of a stationary electromagnetic field is also studied and a comparison is made with the standard short-wave approximation. The results can be applied to the general case of a structured light beams, in flat or curved spaces. Bessel beams are worked out as example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Broad Applicability of Electrochemical Impedance Spectroscopy to the Measurement of Oxygen Nonstoichiometry in Mixed Ion and Electron Conductors

Oxygen non-stoichiometry is a fundamental feature of mixed ion and electron conductors (MIECs). In this work a general electrochemical method for determining non-stoichiometry in thin film MIECs, via measurement of the chemical capacitance, is demonstrated using ceria and ceria-zirconia (Ce 0.8 Zr 0.2 O 2-δ ) as representative materials. A.C. impedance data are collected from both materials at high temperature (750-900 °C) under reducing conditions with oxygen partial pressure (pO 2 ) in the range 10-13 to 10-20 atm. Additional measurements of ceria-zirconia films are made under relatively oxidizing conditions with pO 2 in the range 0.2 to 10 -4 atm and temperatures of 800-900 °C. Under reducing conditions, the impedance spectra are described by a simple circuit in which a resistor is in series with a resistor and capacitor in parallel, and thickness dependent measurements are used to resolve the capacitance into interfacial and chemical terms. Under more oxidizing conditions, the impedance spectra (of Ce 0.8 Zr 0.2 O 2-δ ) reveal an additional diffusional feature, which enables determination of the ionic resistance of the film in addition to the capacitance, and hence the transport properties. A generalized mathematical formalism is presented for recovering the non-stoichiometry from the chemical capacitance, without recourse to defect chemical models. The ceria non-stoichiometry values are in good agreement with literature values determined by thermogravimetric measurements but display considerably less scatter and are collected on considerably shorter timescales. Here, the thermodynamic analysis of Ce 0.8 Zr 0.2 O 2-δ corroborates earlier findings that introduction of Zr into ceria enhances its reducibility.

08 HYDROGEN↗

DOE OSTI2021

Impact of the coordination of multiple Lewis acid functions on the electronic structure and v n configuration of a metal center

Here, the covalent bond classification (CBC) method represents a molecule as ML l X x Z z by evaluating the total number of L, X and Z functions interacting with M. The CBC method is a simplistic approach that is based on the notion that the bonding of a ligating atom (or group of atoms) can be expressed in terms of the number of electrons it contributes to a 2-electron bond. In many cases, the bonding in a molecule of interest can be described in terms of a 2-center 2-electron bonding model and the ML l X x Z z classification can be derived straightforwardly by considering each ligand independently. However, the bonding within a molecule cannot always be described satisfactorily by using a 2-center 2-electron model and, in such situations, the ML l X x Z z classification requires a more detailed consideration than one in which each ligand is treated in an independent manner. The purpose of this article is to provide examples of how the ML l X x Z z classification is obtained in the presence of multicenter bonding interactions. Specific emphasis is given to the treatment of multiple π-acceptor ligands and the impact on the v n configuration, i.e. the number of formally nonbonding electrons on an element of interest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

A National Radiation Oncology Medical Student Clerkship Survey: Didactic Curricular Components Increase Confidence in Clinical Competency

Purpose: Students applying to radiation oncology residency programs complete 1 or more radiation oncology clerkships. This study assesses student experiences and perspectives during radiation oncology clerkships. The impact of didactic components and number of clerkship experiences in relation to confidence in clinical competency and preparation to function as a first-year radiation oncology resident are evaluated. Methods and Materials: An anonymous, Internet-based survey was sent via direct e-mail to all applicants to a single radiation oncology residency program during the 2012-2013 academic year. The survey was composed of 3 main sections including questions regarding baseline demographic information and prior radiation oncology experience, rotation experiences, and ideal clerkship curriculum content. Results: The survey response rate was 37% (70 of 188). Respondents reported 191 unique clerkship experiences. Of the respondents, 27% (19 of 70) completed at least 1 clerkship with a didactic component geared towards their level of training. Completing a clerkship with a didactic component was significantly associated with a respondent's confidence to function as a first-year radiation oncology resident (Wilcoxon rank–sum P=.03). However, the total number of clerkships completed did not correlate with confidence to pursue radiation oncology as a specialty (Spearman ρ P=.48) or confidence to function as a first year resident (Spearman ρ P=.43). Conclusions: Based on responses to this survey, rotating students perceive that the majority of radiation oncology clerkships do not have formal didactic curricula. Survey respondents who completed a clerkship with a didactic curriculum reported feeling more prepared to function as a radiation oncology resident. However, completing an increasing number of clerkships does not appear to improve confidence in the decision to pursue radiation oncology as a career or to function as a radiation oncology resident. These results support further development of structured didactic curricula for the radiation oncology clerkship.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2017

Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations

The representation and storage of two-electron integral tensors are vital in large- scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this paper, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of atomic basis set N_b ranging from ~ 100 up to ~ 2, 000, the observed numerical scaling of our implementation shows O(N_b^{2.5~3}) versus O(N_b^{3~4}) of single CD in most of other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic-orbital (AO) two-electron integral tensor from O(N_b^4) to O(N_b^2 log_{10}(N_b)) with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled- cluster formalism employing single and double excitations (CCSD) on several bench- mark systems including the C_{60} molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10^{-4} to 10^{-3} to give acceptable compromise between efficiency and accuracy.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2014

Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory

We revisit the calculation of analytic derivative couplings for configuration interaction singles (CIS), and derive and implement these couplings for its spin-flip variant for the first time. Our algorithm is closely related to the CIS analytic energy gradient algorithm and should be straightforward to implement in any quantum chemistry code that has CIS analytic energy gradients. The additional cost of evaluating the derivative couplings is small in comparison to the cost of evaluating the gradients for the two electronic states in question. Incorporation of an exchange-correlation term provides an ad hoc extension of this formalism to time-dependent density functional theory within the Tamm-Dancoff approximation, without the need to invoke quadratic response theory or evaluate third derivatives of the exchange-correlation functional. Application to several different conical intersections in ethylene demonstrates that minimum-energy crossing points along conical seams can be located at substantially reduced cost when analytic derivative couplings are employed, as compared to use of a branching-plane updating algorithm that does not require these couplings. Application to H{sub 3} near its D{sub 3h} geometry demonstrates that correct topology is obtained in the vicinity of a conical intersection involving a degenerate ground state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2011

Baryons and baryonic matter in the large N{sub c} and heavy quark limits

This paper explores properties of baryons and finite density baryonic matter in an artificial world in which N{sub c}, the number of colors, is large and the quarks of all species are degenerate and much larger than {Lambda}{sub QCD}. It has long been known that in large N{sub c} quantum chromodynamics (QCD), baryons composed entirely of heavy quarks are accurately described in the mean-field approximation. However, the detailed properties of baryons in the combined large N{sub c} and heavy-quark limits have not been fully explored. Here some basic properties of baryons are computed using a variational approach. At leading order in both the large N{sub c} and heavy-quark expansions the baryon mass is shown to be M{sub baryon}{approx_equal}N{sub c}M{sub Q}(1-0.054 26{alpha}-tilde{sub s}{sup 2}), where {alpha}-tilde{sub s}{identical_to}N{sub c}{alpha}s. The baryon form factor is also computed. Baryonic matter, the analog of nuclear matter in this artificial world, should also be well described in the mean-field approximation. In the special case where all baryons have an identical spin-flavor structure, it is shown that in the formal heavy-quark and large N{sub c} limit interactions between baryons are strictly repulsive at low densities. The energy per baryon is computed in this limit and found to be exponentially small. It is shown that when the restriction to baryons with an identical spin-flavor structure is dropped, a phase of baryonic matter exists with a density of 2N{sub f} times that for the restricted case but with the same energy (where N{sub f} is the number of degenerate flavors). It is shown that this phase is at least metastable.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2013

Assessing the Quality of Bioforensic Signatures

We present a mathematical framework for assessing the quality of signature systems in terms of fidelity, cost, risk, and utility—a method we refer to as Signature Quality Metrics (SQM). We demonstrate the SQM approach by assessing the quality of a signature system designed to predict the culture medium used to grow a microorganism. The system consists of four chemical assays designed to identify various ingredients that could be used to produce the culture medium. The analytical measurements resulting from any combination of these four assays can be used in a Bayesian network to predict the probabilities that the microorganism was grown using one of eleven culture media. We evaluated fifteen combinations of the signature system by removing one or more of the assays from the Bayes network. We demonstrated that SQM can be used to distinguish between the various combinations in terms of attributes of interest. The approach assisted in clearly identifying assays that were least informative, largely in part because they only could discriminate between very few culture media, and in particular, culture media that are rarely used. There are limitations associated with the data that were used to train and test the signature system. Consequently, our intent is not to draw formal conclusions regarding this particular bioforensic system, but rather to illustrate an analytical approach that could be useful in comparing one signature system to another.

Bayesian networks↗

DOE OSTI2014

On systems having Poincaré and Galileo symmetry

Using the wave equation in d≥1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d=1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d>1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell’s equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Optoelectronic properties of candidate photovoltaic Cu 2 PbSiS 4 , Ag 2 PbGeS 4 and KAg 2 SbS 4 semiconductors

High temperature synthesis and optical band gaps are reported for three candidate photovoltaic earth-abundant Cu 2 PbSiS 4 , Ag 2 PbGeS 4 and KAg 2 SbS 4 semiconductors. The reported synthesis method is found to be more advantageous for KAg 2 SbS 4 compared to the literature reported synthesis utilizing supercritical ammonia as a reaction medium, which produces a mixture of chalcogenide products. Based on optical diffuse reflectance data, Cu 2 PbSiS 4 , Ag 2 PbGeS 4 and KAg 2 SbS 4 have band gaps in the 1.6–1.8 eV range, and are shown to be stable in ambient air for a period of 6 weeks, making them attractive candidates for solar cell applications. Density functional theory (DFT) calculations indicate indirect band gaps for Cu 2 PbSiS 4 and KAg 2 SbS 4 , and a nearly direct band gap for Ag 2 PbGeS 4 with the calculated difference between indirect and direct gaps of only 30 meV. The p-type semiconducting behavior of Cu 2 PbSiS 4 , Ag 2 PbGeS 4 is also verified by the transport measurments. The 3D connectivity of the polyanionic networks in these compounds results in dispersive valence and conduction bands, which is especially noticeable for KAg 2 SbS 4 . This fact is in part attributed to the presence of formally pentavalent SbV in this compound leading to empty Sb 5s orbitals in the conduction band. Finally, we discuss the potential of Cu 2 PbSiS 4 , Ag 2 PbGeS 4 and KAg 2 SbS 4 for photovoltaic applications based on synthesis, stability, band gap and electronic structure considerations.

14 SOLAR ENERGY↗

DOE OSTI2014

Controversial electronic structures and energies of Fe{sub 2}, Fe{sub 2}{sup +}, and Fe{sub 2}{sup −} resolved by RASPT2 calculations

The diatomic molecule Fe{sub 2} was investigated using restricted active space second-order perturbation theory (RASPT2). This molecule is very challenging to study computationally because predictions about the ground state and excited states depend sensitively on the choice of the quantum chemical method. For Fe{sub 2} we show that one needs to go beyond a full-valence active space in order to achieve even qualitative agreement with experiment for the dissociation energy, and we also obtain a smooth ground-state potential curve. In addition we report the first multireference study of Fe{sub 2}{sup +}, for which we predict an {sup 8}Σ{sub u}{sup −} ground state, which was not predicted by previous computational studies. By using an active space large enough to remove the most serious deficiencies of previous theoretical work and by explicitly investigating the interpretations of previous experimental results, this study elucidates previous difficulties and provides – for the first time – a qualitatively correct treatment of Fe{sub 2}, Fe{sub 2}{sup +}, and Fe{sub 2}{sup −}. Moreover, this study represents a record in terms of the number or active electrons and active orbitals in the active space, namely 16 electrons in 28 orbitals. Conventional CASPT2 calculations can be performed with at most 16 electrons in 16 orbitals. We were able to overcome this limit by using the RASPT2 formalism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

ON GENERAL RELATIVISTIC UNIFORMLY ROTATING WHITE DWARFS

The properties of uniformly rotating white dwarfs (RWDs) are analyzed within the framework of general relativity. Hartle's formalism is applied to construct the internal and external solutions to the Einstein equations. The white dwarf (WD) matter is described by the relativistic Feynman-Metropolis-Teller equation of state which generalizes that of Salpeter by taking into account the finite size of the nuclei, and the Coulomb interactions as well as electroweak equilibrium in a self-consistent relativistic fashion. The mass M, radius R, angular momentum J, eccentricity {epsilon}, and quadrupole moment Q of RWDs are calculated as a function of the central density {rho} {sub c} and rotation angular velocity {Omega}. We construct the region of stability of RWDs (J-M plane) taking into account the mass-shedding limit, inverse {beta}-decay instability, and the boundary established by the turning points of constant J sequences which separates stable from secularly unstable configurations. We found the minimum rotation periods {approx}0.3, 0.5, 0.7, and 2.2 s and maximum masses {approx}1.500, 1.474, 1.467, 1.202 M {sub Sun} for {sup 4}He, {sup 12}C, {sup 16}O, and {sup 56}Fe WDs, respectively. By using the turning-point method, we found that RWDs can indeed be axisymmetrically unstable and we give the range of WD parameters where this occurs. We also construct constant rest-mass evolution tracks of RWDs at fixed chemical composition and show that, by losing angular momentum, sub-Chandrasekhar RWDs (mass smaller than maximum static one) can experience both spin-up and spin-down epochs depending on their initial mass and rotation period, while super-Chandrasekhar RWDs (mass larger than maximum static one) only spin up.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Application of the general thermal field model to simulate the behaviour of nanoscale Cu field emitters

Strong field electron emission from a nanoscale tip can cause a temperature rise at the tip apex due to Joule heating. This becomes particularly important when the current value grows rapidly, as in the pre-breakdown (the electrostatic discharge) condition, which may occur near metal surfaces operating under high electric fields. The high temperatures introduce uncertainties in calculations of the current values when using the Fowler–Nordheim equation, since the thermionic component in such conditions cannot be neglected. In this paper, we analyze the field electron emission currents as the function of the applied electric field, given by both the conventional Fowler–Nordheim field emission and the recently developed generalized thermal field emission formalisms. We also compare the results in two limits: discrete (atomistic simulations) and continuum (finite element calculations). The discrepancies of both implementations and their effect on final results are discussed. In both approaches, the electric field, electron emission currents, and Joule heating processes are simulated concurrently and self-consistently. We show that the conventional Fowler–Nordheim equation results in significant underestimation of electron emission currents. We also show that Fowler–Nordheim plots used to estimate the field enhancement factor may lead to significant overestimation of this parameter especially in the range of relatively low electric fields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Heavy ion collisions from $\sqrt{s_{NN}}$ of 62.4 GeV down to 7.7 GeV in the EPOS4 framework

The EPOS4 project is an attempt to construct a realistic model for describing relativistic collisions of different systems, from proton-proton (𝑝⁢𝑝) to nucleus-nucleus (𝐴⁢𝐴), at energies from several TeV per nucleon down to several GeV. We argue that a parallel scattering formalism (as in EPOS4) is relevant for primary scatterings in 𝐴⁢𝐴 collisions above 4 GeV, whereas sequential scattering (cascade) is appropriate below. We present briefly the basic elements of EPOS4, and then investigate heavy ion collisions from 62.4 GeV down to 7.7 GeV, to understand how physics changes with energy, studying in particular the disappearance of the fluid component at low energies.

Monte Carlo methods↗