Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Self consistent field methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

Electronic structure of LaNiO 2 and CaCuO 2 from a self-consistent vertex-corrected GW approach

In this work, the electronic structure of one of the nickelates (LaNiO 2 ) and one of the cuprates (CaCuO 2 ) is studied with three self-consistent GW-based methods: scGW, sc(GW+vertex), and quasiparticle self-consistent GW. Low-energy features obtained in our study are in many respects similar to the features reported in previous density functional theory plus dynamical mean-field theory (DFT+DMFT) studies. Consistent with the DFT+DMFT conclusion, we find LaNiO 2 to be more correlated than CaCuO 2 . However, correlation effects included in our study change the DFT Fermi surface near the Γ point differently from that reported in DMFT studies. Features that are a few electronvolts away from the Fermi level are broader in our calculations than in the DFT+DMFT, which reflects the differences between the DFT and the GW methods. Our results are in qualitative agreement with previous G0W0 results, but the self-consistency results in quantitative differences. Generally, correlation effects are found to be sufficiently weak in both materials, which allows one to use totally ab initio diagrammatic approaches such as sc(GW+Vertex) and to avoid the methods with adjustable parameters (DFT+U or DFT+DMFT). However, the possibility of some strong correlations at low energy that cannot be captured by perturbative methods cannot be completely excluded. For instance, differences in the Fermi surface should be resolved, thus experimental studies are necessary.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Theoretical research program to study chemical reactions in AOTV bow shock tubes

Progress in the development of computational methods for the characterization of chemical reactions in aerobraking orbit transfer vehicle (AOTV) propulsive flows is reported. Two main areas of code development were undertaken: (1) the implementation of CASSCF (complete active space self-consistent field) and SCF (self-consistent field) analytical first derivatives on the CRAY X-MP; and (2) the installation of the complete set of electronic structure codes on the CRAY 2. In the area of application calculations the main effort was devoted to performing full configuration-interaction calculations and using these results to benchmark other methods. Preprints describing some of the systems studied are included.

Taylor, P.↗

Toward continuum gyrokinetic study of high-field mirrors

High-temperature superconducting (HTS) magnetic mirrors under development exploit strong fields with high mirror ratio to compress loss cones and enhance confinement and may offer cheaper, more compact fusion power plant candidates. This new class of devices could exhibit largely unexplored interchange and gradient-driven modes. Such instabilities, and methods to stabilize them, can be studied with gyrokinetics, given the strong magnetization and prevalence of kinetic effects. Our focus here is to (a) determine if oft-used gyrokinetic models for open field lines produce the electron-confining (Pastukhov) electrostatic potential and (b) examine and address challenges faced by gyrokinetic codes in studying HTS mirrors. Here, we show that a one-dimensional limit of said models self-consistently develops a potential qualitatively approaching the analytical Pastukhov level. Additionally, we describe the computational challenges of studying high mirror ratios with open field line gyrokinetic solvers and offer a force softening method to mitigate small time steps needed for time integration in colossal magnetic field gradients produced by HTS coils, providing a 19X speedup.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Hybrid algorithm for the time-dependent Hartree–Fock method using the Yang–Baxter equation on quantum computers *

Abstract The time-dependent Hartree–Fock (TDHF) method is an approach to simulate the mean field dynamics of electrons within the assumption that the electrons move independently in their self-consistent average field and within the space of single Slater determinants. One of the major advantages of performing time dynamics within Hartree–Fock theory is the free fermionic nature of the problem, which makes TDHF classically simulatable in polynomial time. Here, we present a hybrid TDHF implementation for quantum computers. This quantum circuit grows with time; but with our recent work on circuit compression via the Yang–Baxter equation (YBE), the resulting circuit is constant depth. This study provides a new way to simulate TDHF with the aid of a quantum device as well as provides a new direction for the application of YBE symmetry in quantum chemistry simulations.

97 MATHEMATICS AND COMPUTING↗

Nonunitary Variational Quantum Eigensolver with the Localized Active Space Method and Cost Mitigation

Accurately describing strongly correlated systems with affordable quantum resources remains a central challenge for quantum chemistry applications on near and intermediate term quantum computers. The localized active space self-consistent field (LASSCF) approximates the complete active space self-consistent field (CASSCF) by generating active space-based wave functions within specific fragments while treating interfragment correlation with mean-field approach, hence is computationally less expensive. Hardware-efficient ansatzes (HEA) offer affordable and shallower circuits, yet they often fail to capture the necessary correlation. Previously, Jastrow-factor-inspired nonunitary qubit operators were proposed to use with HEA for variational quantum eigensolver (VQE) calculations (so-called nuVQE), as they do not increase circuit depths and recover correlation beyond the mean-field level for Hartree–Fock initial states. Here, in this study, we explore running nuVQE with LASSCF as the initial state. The method, named LAS-nuVQE, is shown to recover interfragment correlations, reach chemical accuracy with a small number of gates (<70) in both H 4 and square cyclobutadiene (C 4 H 4 ), and produces more accurate energetics than its HEA counterparts at all circuit depths. To further address the inherent symmetry-breaking in HEA, we implemented spin-constrained LAS-nuVQE to extend the capabilities of HEA further and show spin-pure results for square cyclobutadiene. We also mitigate the increased measurement overhead of nuVQE via Pauli grouping and shot-frugal sampling, reducing measurement costs by up to 2 orders of magnitude compared to ungrouped operator, and show that one can achieve better accuracy with a small number of shots (10 3–4 ) per one expectation value calculation compared to noiseless simulations with one or two orders of magnitude more shots. Finally, wall clock time estimates show that, with our measurement mitigation protocols, nuVQE becomes a cheaper and more accurate alternative than vanilla VQE with HEA. Taken together, these developments illustrate a practical pathway toward performing multireference chemical simulations with accuracy and affordable resources on today’s quantum hardware, achieving both accuracy and affordability in challenging correlated systems.

Wang, Qiaohong [Univ. of Chicago, IL (United State↗

The role and behavior of spin in gravitational physics

A self-consistent method of introducing spin into any Lagrangian based theory of gravitation was developed. The metric variation of the Lagrangian in the theory leads to an improved energy-momentum tensor which represents the source term in the gravitational field equations. The goal of the research is the construction of a theory general enough to be used to investigate spin effects in astrophysical objects and cosmology, and also to serve as a basis for discussion of the theoretical ideas tested by the NASA Gyroscope Experiment (aboard Gravity Probe B). Specific accomplishments in the following areas are summarized: the inclusion of electromagnetism into the variational principle for spinning matter, formulation of a self-consistent theory for the case of a fluid in which particle production processes occur, and the derivation of the Raychaudhuri equation in the case of spinning matter.

Ray, John R.↗

Evaluation of the critical behavior near ferromagnetic to paramagnetic phase transition in CrTe 1-x Se x alloys: An experimental study

For this study, we used the conventional solid-state reaction method to prepare stoichiometric samples of CrTe 1-x Se x , where 0 ≤ x ≤ 0.10, and investigated the structural and critical behavior of the prepared samples. Room temperature powder X-ray diffraction, along with Rietveld refinement, revealed the emergence of the NiAs structure with P6 3 /mmc (194) space group with increasing Se substitution. The high-temperature linear fit to inverse of the dc-susceptibility versus temperature for the mother sample resulted in an effective moment of 3.65μ B Cr with Curie-Weiss temperature near 335K, which is slightly higher than the Tc of ~332K obtained from the inflection point of magnetization versus temperature. Magnetization isotherms were employed to investigate the critical behavior of ferromagnetic CrTe 1-x Se x with 0.0 ≤ x ≤ 0.10 near their Curie temperatures (Tc). The magnetic behavior near Tc was found to follow 3D mean-field critical exponents with a second-order phase transition in all samples investigated. We fine-tuned the critical exponents (β, γ, and δ) using a combination of an iteration technique, the Kouvel-Fisher method, and modified Arrott plots. All samples follow a mean field behavior, with Tc ranging from 298 to 340K. The acquired values exhibit self-consistency, as indicated by the results from the Widom scaling relation. Furthermore, the magnetization isotherms exhibit a universal scaling behavior, providing additional credence to the calculated critical exponents.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Benchmarking an Embedded Adaptive Sampling Configuration Interaction Method for Surface Reactions: H 2 Desorption from and CH 4 Dissociation on Cu(111)

Embedded (emb-) correlated wavefunction (CW) theory enables accurate assessments of both ground- and excited-state reaction mechanisms involved in heterogeneous catalysis. Embedded multireference second-order perturbation theory (emb-MRPT2) based on reference wavefunctions generated via embedded complete active space self-consistent field (emb-CASSCF) theory is currently state-of-the-art. However, the factorial scaling of CASSCF limits the size of active space and the complexity of systems that can be studied. In this work, we assess the efficacy of an alternative CW method, adaptive sampling configuration interaction (ASCI)–which enables large active spaces to be used–for studying surface reactions. We couple ASCI with density functional embedding theory (DFET) and benchmark its performance for two reactions: H 2 desorption from and CH 4 dissociation on the Cu(111) surface. Unlike embedded complete active space second-order perturbation theory (emb-CASPT2) that accurately reproduces a measured H 2 desorption barrier, embedded ASCI, using a very large active space (though one that still comprises a small portion of the full set of orbitals) fails to do so. Adding an extra correlation term from embedded Møller–Plesset second-order perturbation theory (emb-MP2) improves the desorption barrier and endothermicity predictions. Thus, the inaccuracy of embedded ASCI comes from the missing dynamic correlation from the many other electrons and orbitals not included in the active space. For CH 4 dissociation, again embedded ASCI overestimates the dissociation barrier compared to emb-CASPT2 predictions. Adding dynamic correlation from emb-MP2 helps correct the barrier. However, this composite approach suffers from double counting of correlation within embedded ASCI followed by emb-MP2 calculations. We therefore conclude that the state-of-the-art emb-MRPT2 based on reference wavefunctions generated via emb-CASSCF remains the method of choice for studying surface reactions. emb-ASCI is useful when large active spaces beyond the limit of emb-CASSCF are essential, such as to study complex surface reactions with significant multiconfigurational character (static correlation) but weak dynamic correlation.

08 HYDROGEN↗

Strategies to Obtain Reliable Energy Landscapes from Embedded Multireference Correlated Wavefunction Methods for Surface Reactions

Embedded correlated wavefunction (ECW) theory is a powerful tool for studying ground- and excited-state reaction mechanisms and associated energetics in heterogeneous catalysis. Several factors are important to obtaining reliable ECW energies, critically the construction of consistent active spaces (ASs) along reaction pathways when using a multireference correlated wavefunction (CW) method that relies on a subset of orbital spaces in the configuration interaction expansion to account for static electron correlation, e.g., complete AS self-consistent field theory, in addition to the adequate partitioning of the system into a cluster and environment, as well as the choice of a suitable basis set and number of states included in excited-state simulations. Here, in this work, we conducted a series of systematic studies to develop best-practice guidelines for ground- and excited-state ECW theory simulations, utilizing the decomposition of NH 3 on Pd(111) as an example. We determine that ECW theory results are relatively insensitive to cluster size, the aug-cc-pVDZ basis set provides an adequate compromise between computational complexity and accuracy, and that a fixed-clean-surface approximation holds well for the derivation of the embedding potential. Additionally, we demonstrate that a merging approach, which involves generating ASs from the molecular fragments at each configuration, is preferable to a creeping approach, which utilizes ASs from adjacent structures as an initial guess, for the generation of consistent potential energy curves involving open-d-shell metal surfaces, and, finally, we show that it is essential to include bands of excited states in their entirety when simulating excited-state reaction pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Benchmark full configuration-interaction calculations on H2O, F- and F

Full configuration-interaction calculations are reported, and compared to other methods, for H2O at its equilibrium geometry and at two geometries with the H-O bonds stretched. Since the percentage of the self-consistent field (SCF) reference in the full configuration-interaction (FCI) wave function decreases greatly with the bond elongation, the accuracy of techniques based on a single reference do not compare well with the FCI results. However, the results from a complete active space SCF/multireference configuration-interaction (CASSCF/MRCI) treatment are in good agreement with the FCI. Correlation effects in F compared to Ne are far more similar than for F- compared to Ne, despite F- and Ne being isoelectronic. Since the importance of higher than double excitations is more important for F- than F, a very high percentage of the correlation must be obtained to accurately compute the electron affinity. In a CASSCF/MRCI treatment the higher than quadruple excitations contribute 0.02 eV to the electron affinity (EA), even for modest basis sets.

Bauschlicher, C. W., Jr.↗

Benchmark full configuration-interaction calculations on H2O, F, and

Full configuration-interaction calculations are reported, and compared to other methods, for H2O at its equilibrium geometry and at two geometries with the H-O bonds stretched. Since the percentage of the self-consistent field (SCF) reference in the full configuration-interaction (FCI) wave function decreases greatly with the bond elongation, the accuracy of techniques based on a single reference do not compare well with the FCI results. However, the results from a complete active space SCF/multireference configuration-interaction (CASSCF/MRCI) treatment are in good agreement with the FCI. Correlation effects in F compared to Ne are far more similar than for Fcompared to Ne, despite F- and Ne being isoelectronic. Since the importance of higher than double excitations is more important for F- than F, a very high percentage of the correlation must be obtained to accurately compute the electron affinity. In a CASSCF/MRCI treatment the higher than quadruple excitations contribute 0.02 eV to the electron affinity (EA), even for modest basis sets.

Bauschlicher, C. W., Jr.↗

Generalized spin σ -SCF method

We introduce a generalization of the σ-SCF method to approximate noncollinear spin ground and excited single-reference electronic states by minimizing the Hamiltonian variance. The new method is based on the σ-SCF method, originally proposed by Ye et al. [J. Chem. Phys. 147, 214104 (2017)], and provides a prescription to determine ground and excited noncollinear spin states on an equal footing. Our implementation was carried out utilizing an initial simulated annealing stage followed by a mean-field iterative self-consistent approach to simplify the cumbersome search introduced by generalizing the spin degrees of freedom. The simulated annealing stage ensures a broad exploration of the Hilbert space spanned by the generalized spin single-reference states with random complex element-wise rotations of the generalized density matrix elements in the simulated annealing stage. The mean-field iterative self-consistent stage employs an effective Fockian derived from the variance, which is utilized to converge tightly to the solutions. This process helps us to easily find complex spin structures, avoiding manipulating the initial guess. As proof-of-concept tests, we present results for Hn (n = 3–7) planar rings and polyhedral clusters with geometrical spin frustration. We show that most of these systems have noncollinear spin excited states that can be interpreted in terms of geometric spin frustration. These states are not directly targeted by energy minimization methods, which are meant to converge to the ground state. This stresses the capability of the σ-SCF methodology to find approximate noncollinear spin structures as mean-field excited states.

Chemistry↗

A new look at rainfall fluctuations and scaling properties of spatial rainfall using orthogonal wavelets

It has been observed that the finite-dimensional distribution functions of rainfall cannot obey simple scaling laws due to rainfall intermittency (mixed distribution with an atom at zero) and the probability of rainfall being an increasing function of area. Although rainfall fluctuations do not suffer these limitations, it is interesting to note that very few attempts have been made to study them in terms of their self-similarity characteristics. This is due to the lack of unambiguous definition of fluctuations in multidimensions. This paper shows that wavelet transforms offer a convenient and consistent method for the decomposition of inhomogeneous and anisotropic rainfall fields in two dimensions and that the components of this decomposition can be looked at as fluctuations of the rainfall field. It is also shown that under some mild assumptions, the component fields can be treated as homogeneous and thus are amenable to second-order analysis, which can provide useful insight into the nature of the process. The fact that wavelet transforms are a space-scale method also provides a convenient tool to study scaling characteristics of the process. Orthogonal wavelets are used, and these properties are investigated for a squall-line storm to study the presence of self-similarity.

Kumar, Praveen↗

Spin-projected and extended SCF calculations.

Spin restricted, unrestricted, projected unrestricted and extended SCF wave functions energies compared, discussing calculation method for spin extended SCF functions

WAVE FUNCTION↗

Cosmological perturbation theory for large scale structure in phase space

We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of negligible velocity dispersion underlying the Standard Perturbation Theory (SPT). We apply the new method to rederive the usual SPT kernels up to third order in the perturbative expansion. We also show that a counterterm, identical to the one introduced by standard Effective Field Theory (EFT) methods, naturally arises within our framework. We finish by making a precise connection to EFT techniques, which reveals the necessity of the EFTofLSS to self-consistently model the long-wavelength fluid, and illustrates the importance of having theoretical control over short distance fluctuations.

Cosmological perturbation theory in GR and beyond↗

Electric Field Reconstruction in the Image Plane of a High-Contrast Coronagraph Using a Set of Pinholes around the Lyot Plane

In a setup similar to the self coherent camera, we have added a set of pinholes in the diffraction ring of the Lyot plane in a high-contrast stellar Lyot coronagraph. We describe a novel complex electric field reconstruction from image plane intensity measurements consisting of light in the coronagraph's dark hole interfering with light from the pinholes. The image plane field is modified by letting light through one pinhole at a time. In addition to estimation of the field at the science camera, this method allows for self-calibration of the probes by letting light through the pinholes in various permutations while blocking the main Lyot opening. We present results of estimation and calibration from the High Contrast Imaging Testbed along with a comparison to the pair-wise deformable mirror diversity based estimation technique. Tests are carried out in narrow-band light and over a composite 10% bandpass.

coronagraphs↗

Kinetic simulations of collision-less plasmas in open magnetic geometries

Laboratory plasmas in open magnetic geometries can be found in many different applications such as (a) scrape-of-layer (SOL) and divertor regions in toroidal confinement fusion devices, (b) linear divertor simulators, (c) plasma-based thrusters and (d) magnetic mirrors etc. A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along flux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic particle-in-cell (PIC) simulations can be applied but at the expense of large computational effort. A common way to resolve this is to use a hybrid approach: kinetic ions and fluid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (a) the effect of non-uniform magnetic fields, (b) finite fully-absorbing boundaries for the particles and (c) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in a state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. The results show that the effect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric field is calculated and is shown to modify the ion velocity distribution function in a manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, the inclusion of a Monte Carlo based Fokker-Planck collision operator is discussed in the context of future work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Atomic isotropic hyperfine properties for first row elements (B–F) revisited

Benchmark quality isotropic hyperfine properties have been obtained for first row elements (B–F) using a systematic composite approach consisting of a sequence of core/valence correlation consistent basis sets, up through aug-cc-pCV8Z, along with configuration interaction and coupled cluster theory methods. The best nonrelativistic final values (in MHz) are 10.64 (B), 20.22 (C), 10.59 (N), –31.74 (O), and 318.30 (F) and are in very good agreement with available experimental values for these difficult-to-describe properties. Agreement is especially close in the case of N, which has the most accurate experimental value. The spin densities derived from the best composite level of theory were found to closely follow a simple quadratic scaling with the atomic number, Z. Finally, observed convergence rates in the 1-particle and n-particle expansions obtained here may be useful in judging likely accuracy that can be expected in studies of molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗