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DOE OSTI2017

Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon

We present a new efficient way to perform hybrid density functional theory (DFT)-based electronic structure calculations. The new method uses an interpolative separable density fitting (ISDF) procedure to construct a set of numerical auxiliary basis vectors and a compact approximation of the matrix consisting of products of occupied orbitals represented in a large basis set such as the planewave basis. Such an approximation allows us to reduce the number of Poisson solves from O ($N$ $^{2}_{ϵ}$) to O ( N ϵ ) when we apply the exchange operator to occupied orbitals in an iterative method for solving the Kohn–Sham equations, where Ne is the number of electrons in the system to be studied. We show that the ISDF procedure can be carried out in O ($N$ $^{3}_{ϵ}$) operations, with a much smaller preconstant compared to methods used in existing approaches. When combined with the recently developed adaptively compressed exchange (ACE) operator formalism, which reduces the number of times the exchange operator needs to be updated, the resulting ACE-ISDF method significantly reduces the computational cost associated with the exchange operator by nearly 2 orders of magnitude compared to existing approaches for a large silicon system with 1000 atoms. We demonstrate that the ACE-ISDF method can produce accurate energies and forces for insulating and metallic systems and that it is possible to obtain converged hybrid functional calculation results for a 1000-atom bulk silicon within 10 min on 2000 computational cores. We also show that ACE-ISDF can scale to 8192 computational cores for a 4096-atom bulk silicon system. We use the ACE-ISDF method to geometrically optimize a 1000-atom silicon system with a vacancy defect using the HSE06 functional and computes its electronic structure. Here, we find that that the computed energy gap from the HSE06 functional is much closer to the experimental value compared to that produced by semilocal functionals in the DFT calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Free-free matrix-elements for two-photon opacity

Recent opacity measurements have inspired a close study of the two-photon contributions to the opacity of hot plasmas. The absorption and emission of radiation is controlled by dipole matrix-elements of electrons in an atom or ion. This paper describes two independent methods to calculate matrix-elements needed for the two-photon opacity and tests the results by the f-sum rule. The usual f-sum rule is extended to a matrix f-sum that offers a rigorous test for bound-bound, bound-free and free-free transitions. An additional higher-order sum-rule for the two-photon transition amplitudes is described. In this work, we obtain a simple parametric representation of a key plasma density effect on the matrix-elements. The perturbation theory calculation of two-photon cross-sections is compared to an independent method based on the solution of the time-dependent Schroedinger equation for an atom or ion in a high-frequency electromagnetic field. This is described as a high frequency Stark effect or AC Stark effect. Two-photon cross sections calculated with the AC Stark code agree with perturbation theory to within about 5%. In addition to this cross check, the AC Stark code is well suited to evaluating important questions such as the variation of two-photon opacity for different elements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2013

An accurate and linear-scaling method for calculating charge-transfer excitation energies and diabatic couplings

Quantum-mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the frozen density embedding formulation of subsystem density-functional theory; subsequently, in a post-SCF calculation, the full-electron Hamiltonian and overlap matrix elements among the charge-localized states are evaluated with an algorithm which takes full advantage of the subsystem DFT density partitioning technique. The method is benchmarked against coupled-cluster calculations and achieves chemical accuracy for the systems considered for intermolecular separations ranging from hydrogen-bond distances to tens of Angstroms. Numerical examples are provided for molecular clusters comprised of up to 56 non-covalently bound molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Band gap engineering in finite elongated graphene nanoribbon heterojunctions: Tight-binding model

A simple model based on the divide and conquer rule and tight-binding (TB) approximation is employed for studying the role of finite size effect on the electronic properties of elongated graphene nanoribbon (GNR) heterojunctions. In our model, the GNR heterojunction is divided into three parts: a left (L) part, middle (M) part, and right (R) part. The left part is a GNR of width W{sub L}, the middle part is a GNR of width W{sub M}, and the right part is a GNR of width W{sub R}. We assume that the left and right parts of the GNR heterojunction interact with the middle part only. Under this approximation, the Hamiltonian of the system can be expressed as a block tridiagonal matrix. The matrix elements of the tridiagonal matrix are computed using real space nearest neighbor orthogonal TB approximation. The electronic structure of the GNR heterojunction is analyzed by computing the density of states. We demonstrate that for heterojunctions for which W{sub L} = W{sub R}, the band gap of the system can be tuned continuously by varying the length of the middle part, thus providing a new approach to band gap engineering in GNRs. Our TB results were compared with calculations employing divide and conquer rule in combination with density functional theory (DFT) and were found to agree nicely.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Change of variables as a method to study general β-models: Bulk universality

We consider β matrix models with real analytic potentials. Assuming that the corresponding equilibrium density ρ has a one-interval support (without loss of generality σ = [−2, 2]), we study the transformation of the correlation functions after the change of variables λ{sub i} → ζ(λ{sub i}) with ζ(λ) chosen from the equation ζ{sup ′}(λ)ρ(ζ(λ)) = ρ{sub sc}(λ), where ρ{sub sc}(λ) is the standard semicircle density. This gives us the “deformed” β-model which has an additional “interaction” term. Standard transformation with the Gaussian integral allows us to show that the “deformed” β-model may be reduced to the standard Gaussian β-model with a small perturbation n{sup −1}h(λ). This reduces most of the problems of local and global regimes for β-models to the corresponding problems for the Gaussian β-model with a small perturbation. In the present paper, we prove the bulk universality of local eigenvalue statistics for both one-cut and multi-cut cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Low-energy collective modes of deformed superfluid nuclei within the finite-amplitude method

The major challenge for nuclear theory is to describe and predict global properties and collective modes of atomic nuclei. Of particular interest is the response of the nucleus to a time-dependent external field that impacts the low-energy multipole and β -decay strength, as well as individual nuclear excitations. We propose a method to compute low-lying collective modes in deformed nuclei within the finite-amplitude method (FAM) based on the quasiparticle random-phase approximation (QRPA). By using the analytic property of the response function, we find the QRPA amplitudes by computing the residua of the FAM amplitudes by means of a contour integration around the QRPA poles in a complex frequency plane. We use superfluid nuclear density functional theory with Skyrme energy density functionals, the FAM-QRPA approach, and the conventional matrix formulation of the QRPA. We demonstrate that the complex-energy FAM-QRPA method reproduces low-lying collective states obtained within the conventional matrix formulation of the QRPA theory. Illustrative calculations are performed for the isoscalar monopole strength in deformed 24 Mg and for low-lying $K = 0$ quadrupole vibrational modes of deformed Yb and Er isotopes. The proposed FAM-QRPA approach, in addition to providing a quick estimate of various strength functions, allows one to efficiently calculate the individual QRPA amplitudes of the low-lying collective modes in spherical and deformed nuclei throughout the entire nuclear landscape, in particular shape-vibrational and pairing-vibrational modes and β -decay rates. It can also be employed in microscopic approaches to large-amplitude nuclear collective motion based on the adiabatic self-consistent collective coordinate method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2013

Angular correlations in the inelastic-scattering process {sup 24}Mg(d, d{gamma}){sup 24}Mg at E{sub d} = 15.3 MeV

The double-differential cross sections for the reaction {sup 24}Mg(d, d{gamma}{sub 1.369}){sup 24}Mg at the projectiledeuteron energy of E{sub d} = 15.3 MeV weremeasured for deuteron emission angles in the forward hemisphere. All even spin-tensor components of the density matrix for the 2{sup +} state of the {sup 24}Mg nucleus at 1.369 MeV were reconstructed, and its orientation properties were determined. These experimental results were compared with the results of calculations based on various versions of the coupled-channel method.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2015

Polarisabilities of long conjugated chain molecules with density functional response methods: The role of coupled and uncoupled response

The longitudinal component of the dipole-dipole polarisability of polyacetylene molecules containing 4 to 20 carbon atoms has been calculated with density-functional theory (DFT) response methods. In order to analyse the effect of the uncoupled and coupled contributions to the response matrix, a number of different sets of orbitals were combined with different approximations for the Hessian matrix. This revealed a surprising result: a qualitatively correct increase of the polarisability with the chain length can already be reproduced on the uncoupled level if the response matrix is constructed from Hartree-Fock (HF) or exact-exchange (EXX) DFT orbitals. The nonlocal HF and the local EXX exchange potentials both produce a displacement of charge from the chain ends to the centre of the polyacetylene molecule compared to DFT methods using standard exchange-correlation potentials. In this way, the reduced increase of the transition dipole moments along the molecular axis counteracts the decrease of the occupied-virtual orbital energy gaps and leads to a linear dependence of the polarisabilities (normalised by the number of carbon atoms) on the chain length. A new DFT response approach is tested which utilises unitary transformed Hartree-Fock orbitals as input and which resolves the failure of standard DFT response methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

The multi-configurational time-dependent Hartree approach revisited

The multi-configurational time-dependent Hartree (MCTDH) approach facilitates accurate high-dimensional quantum dynamics simulations. In the approach, the wavefunction is expanded in a direct product of self-adapting time-dependent single-particle functions (SPFs). The equations of motion for the expansion coefficients and the SPFs are obtained via the Dirac-Frenkel variational principle. While this derivation yields well-defined differential equations for the motion of occupied SPFs, singularities in the working equations resulting from unoccupied SPFs have to be removed by a regularization procedure. Here, an alternative derivation of the MCTDH equations of motion is presented. It employs an analysis of the time-dependence of the single-particle density matrices up to second order. While the analysis of the first order terms yields the known equations of motion for the occupied SPFs, the analysis of the second order terms provides new equations which allow one to identify optimal choices for the unoccupied SPFs. The effect of the optimal choice of the unoccupied SPFs on the structure of the MCTDH equations of motion and their regularization is discussed. Generalized equations applicable in the multi-layer MCTDH framework are presented. Finally, the effects resulting from the initial choice of the unoccupied SPFs are illustrated by a simple numerical example.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Sparsity of the electron repulsion integral tensor using different localized virtual orbital representations in local second-order Møller–Plesset theory

Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree–Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller–Plesset theory (MP2), one of the simplest post-HF methods, only the (ia|jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the “ragged list”) and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Here, our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the “fixed sparsity pattern”) for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Ab Initio Design of High-Entropy Thermal/ Environmental Barrier Coatings

Next generation thermal/environmental barrier coatings (TEBC) require carefully balancing various properties including phase stability, thermal conductivity, coefficient of thermal expansion (CTE), mechanical properties, and resistance against hot corrosion and water vapor recession. This work mainly focuses on rapid design of cost-effective high entropy rare-earth disilicates and aluminum garnets to protect SiC-based ceramic matrix composites and nickel-based superalloys in the hot section of gas turbine engines using density functional theory methods. Our calculations identify several low-cost high entropy TEBC exhibiting ultralow thermal conductivity at 1500 K and desirable CTE while maintaining good mechanical properties, including Er1/2Y3/4Yb3/4Si2O7, Gd1/4Er1/4Y3/4Yb3/4Si2O7, Eu1/4Er1/4Y3/4Yb3/4Si2O7, and (Y1/4Gd1/4Er1/4Yb1/4)3Al5O12. This work also aims to gain fundamental understanding of oxygen diffusion in model disilicates. Minimizing oxidizer (such as water vapor and oxygen) permeability through the EBC layer can significantly decrease the growth rate of thermally grown oxide and extend the service life of the coating system. Oxygen diffusion mechanisms including formation energy of defects under varying oxygen conditions and defect migration energy barriers will be presented.

coefficient of thermal expansion↗

DOE OSTI2022

Form factors and spectral densities from Lightcone Conformal Truncation

We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators $\mathcal{O}$ in $\phi^4$ theory in two dimensions. We show how to use the Hamiltonian eigenstates from LCT to obtain form factors that are matrix elements of a local operator $\mathcal{O}$ between single-particle bra and ket states, and we develop methods that significantly reduce errors resulting from the finite truncation of the Hilbert space. We extrapolate these form factors as a function of momentum to the regime where, by crossing symmetry, they are form factors of $\mathcal{O}$ between the vacuum and a two-particle asymptotic scattering state. We also compute the momentum-space time-ordered two-point functions of local operators in LCT. These converge quickly at momenta away from branch cuts, allowing us to indirectly obtain the time-ordered correlator and the spectral density at the branch cuts. We focus on the case where the local operator $\mathcal{O}$ is the trace Θ of the stress tensor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Spin orbit coupling for molecular ab initio density matrix renormalization group calculations: Application to g-tensors

Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1998

MoSi2-Base Hybrid Composite Passed Engine Test

The intermetallics compound molybdenum disilicide (MoSi2) is an attractive high-temperature structural material for advanced engine applications. It has excellent oxidation resistance, a high melting point, relatively low density, and high thermal conductivity, and it is easily machined. Past research'at the NASA Lewis Research Center has resulted in the development of a hybrid composite consisting of a MoSi2 matrix reinforced with silicon nitride (Si3N4) Particulate and silicon carbide (SiC) fibers. This composite has demonstrated attractive strength, toughness, thermal fatigue, and oxidation resistance, including resistance to "pest" oxidation. These properties attracted the interest of the Office of Naval Research and Pratt & Whitney, and a joint NASA/Navy/Pratt & Whitney effort was developed to continue to mature the MoSi2 Composite technology. A turbine blade outer air seal, which was part of the Integrated High Performance Turbine Engine Technology (IHPTET) program, was chosen as a first component on which to focus. The first tasks of the materials development effort were to develop improved processing methods to reduce costs and to use fine-diameter fibers that enable the manufacturing of complex shapes. Tape-casting methods were developed to fully infiltrate the fine SiC fibers with matrix powders. The resulting composites were hot pressed to 100-percent density. Composites with cross-plied fiber architectures with 30 vol. % hi-nicalon SiC fibers and 30 vol. % nitride particles are now made routinely and demonstrate a good balance of properties. The next task entailed the measurement of a wide variety of mechanical properties to confirm the suitability of this composite in engines. In particular, participants in this effort demonstrated that composites made with Hi-Nicalon fibers had strength and toughness properties equal to or better than those of the composites made with the large-diameter fibers that had been used previously. Another critically important property measured was impact resistance. Aircraft engine components require sufficient toughness to resist manufacturing defects, assembly damage, stress concentrations at notches, and foreign object damage. Engine company designers indicated that impact resistance would have to be measured before they would seriously consider these types of composites. The Charpy V-notch test was chosen to assess impact resistance, and both monolithic and composite versions Of MOSi2 were tested from -300 to 1400 C. The results (see the following graphs) show that nitride-particulate-reinforced MoSi2 exhibited impact resistance higher than that of many monolithic ceramics and intermetallics, and that the fiber-reinforced composites had even higher values, approaching that of cast superalloys.

Keith, Theo G., Jr.↗

DOE OSTI2019

Time-evolution methods for matrix-product states

Highlights: • Introductory review of time-evolution methods for matrix-product states. • Detailed description of five state-of-the-art algorithms. • Extended comparison of numerical examples. • Extended error analysis of each algorithm. • Pseudo-code examples towards an implementation where necessary. - Abstract: Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO W{sup I,II} method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Method of evaluating pH using a metallic nanoparticle incorporated nanocomposite-based optical pH sensor

A method for evaluating the pH of an aqueous solution by utilizing the optical properties of a pH sensing material comprised of plurality of optically active nanoparticles dispersed in matrix material. The optically active nanoparticles have an electronic conductivity greater than about 10−1 S/cm and generally have an average nanoparticle diameter of less that about 500 nanometers, and the matrix material is a material which experiences a change in surface charge density over a pH range from 2.0 to 12.0 of at least 1%. The method comprises contacting the pH sensing material and the aqueous solution, illuminating the pH sensing material, and monitoring an optical signal generated through comparison of incident light and exiting light to determine the optical transmission, absorption, reflection, and/or scattering of the pH sensitive material. The optical signal of the pH sensitive material varies in response to the pH of the aqueous solution.

Ohodnicki, Jr., Paul R.↗

DOE OSTI2015

Hybrid detection of lung nodules on CT scan images

Purpose: The diversity of lung nodules poses difficulty for the current computer-aided diagnostic (CAD) schemes for lung nodule detection on computed tomography (CT) scan images, especially in large-scale CT screening studies. We proposed a novel CAD scheme based on a hybrid method to address the challenges of detection in diverse lung nodules. Methods: The hybrid method proposed in this paper integrates several existing and widely used algorithms in the field of nodule detection, including morphological operation, dot-enhancement based on Hessian matrix, fuzzy connectedness segmentation, local density maximum algorithm, geodesic distance map, and regression tree classification. All of the adopted algorithms were organized into tree structures with multi-nodes. Each node in the tree structure aimed to deal with one type of lung nodule. Results: The method has been evaluated on 294 CT scans from the Lung Image Database Consortium (LIDC) dataset. The CT scans were randomly divided into two independent subsets: a training set (196 scans) and a test set (98 scans). In total, the 294 CT scans contained 631 lung nodules, which were annotated by at least two radiologists participating in the LIDC project. The sensitivity and false positive per scan for the training set were 87% and 2.61%. The sensitivity and false positive per scan for the testing set were 85.2% and 3.13%. Conclusions: The proposed hybrid method yielded high performance on the evaluation dataset and exhibits advantages over existing CAD schemes. We believe that the present method would be useful for a wide variety of CT imaging protocols used in both routine diagnosis and screening studies.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

Single-cone finite difference scheme for the (2+1)D Dirac von Neumann equation

An explicit finite difference scheme is presented for the von Neumann equation for (2+1)D Dirac fermions. It is founded upon a staggered space–time grid which ensures a single-cone energy dispersion and performs the time-derivative in one sweep using a three-step leap-frog procedure. It enables a space–time-resolved numerical treatment of the mixed-state dynamics of Dirac fermions within the effective single-particle density matrix formalism. Energy-momentum dispersion, stability and convergence properties are derived. Elementary numerical tests to demonstrate stability properties use parameters which pertain to topological insulator surface states. A method for the simulation of charge injection from an electric contact is presented and tested numerically. Potential extensions of the scheme to a Dirac–Lindblad equation, real-space–time Green's function formulations, and higher-order finite-difference schemes are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗