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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen–Cooper–Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. Here, the method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree–Fock based electronic structure methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Geminal embedding scheme for optimal atomic basis set construction in correlated calculations

We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out from its environment, while the entire system (atom and environment) is described by a Slater determinant or its antisymmetrized geminal power (AGP) extension. The embedding procedure described here allows for the systematic and consistent contraction of the primitive basis set into geminal embedded orbitals (GEOs), with a dramatic reduction of the number of variational parameters necessary to represent the many-body wave function, for a chosen target accuracy. Within the variational Monte Carlo method, the Slater or AGP part is determined by a variational minimization of the energy of the whole system in presence of a flexible and accurate Jastrow factor, representing most of the dynamical electronic correlation. The resulting GEO basis set opens the way for a fully controlled optimization of many-body wave functions in electronic structure calculation of bulk materials, namely, containing a large number of electrons and atoms. We present applications on the water molecule, the volume collapse transition in cerium, and the high-pressure liquid hydrogen.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Time-dependent projected Hartree-Fock

Projected Hartree-Fock (PHF) has recently emerged as an alternative approach to describing degenerate systems where static correlation is abundant, when the spin-symmetry is projected. Here, we derive a set of linearized time-dependent equations for PHF in order to be able to access excited states. The close connection of such linear-response time-dependent PHF (TDPHF) to the stability condition of a PHF wave function is discussed. Expanding this analysis also makes it possible to give analytical expressions for the projected coupling terms of Hamiltonian and overlaps between excited Slater determinants. TDPHF with spin-projection (TDSUHF) and its Tamm-Dancoff approximation are benchmarked for several electronically degenerate molecules including the dissociating H{sub 2}, F{sub 2} and O{sub 3} at equilibrium, and the distorted ethylene. It is shown that they give consistently better descriptions of excited states than does time-dependent HF (TDHF). Furthermore, we demonstrate that they offer not only singly but also doubly excited states, which naturally arise upon spin-projection. We also address the thermodynamic limit of TDSUHF, using non-interacting He gas. While TDPHF singly excited states tend to converge to those of HF with the size of the system due to the lack of size-extensivity of PHF, doubly excited states remain reasonable even at the thermodynamic limit. We find that the overall performance of our method is systematically better than the regular TDHF in many cases at the same computational scaling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

A hybrid configuration interaction treatment based on seniority number and excitation schemes

We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitation-based procedure is more suitable) but show static (strong) correlation at other arrangements (where the seniority-number technique is preferred). The hybrid method amends the shortcomings of both individual determinant selection procedures, yielding correct shapes of potential energy curves with results closer to those provided by the full configuration interaction method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Excited states from quantum Monte Carlo in the basis of Slater determinants

Building on the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm introduced recently by Booth et al. [J. Chem. Phys. 131, 054106 (2009)] to compute the ground state of correlated many-electron systems, an extension to the computation of excited states (exFCIQMC) is presented. The Hilbert space is divided into a large part consisting of pure Slater determinants and a much smaller orthogonal part (the size of which is controlled by a cut-off threshold), from which the lowest eigenstates can be removed efficiently. In this way, the quantum Monte Carlo algorithm is restricted to the orthogonal complement of the lower excited states and projects out the next highest excited state. Starting from the ground state, higher excited states can be found one after the other. The Schrödinger equation in imaginary time is solved by the same population dynamics as in the ground state algorithm with modified probabilities and matrix elements, for which working formulae are provided. As a proof of principle, the method is applied to lithium hydride in the 3-21G basis set and to the helium dimer in the aug-cc-pVDZ basis set. It is shown to give the correct electronic structure for all bond lengths. Much more testing will be required before the applicability of this method to electron correlation problems of interesting size can be assessed.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1984

The importance and attainment of accurate absolute radiometric calibration

The importance of accurate absolute radiometric calibration is discussed by reference to the needs of those wishing to validate or use models describing the interaction of electromagnetic radiation with the atmosphere and earth surface features. The in-flight calibration methods used for the Landsat Thematic Mapper (TM) and the Systeme Probatoire d'Observation de la Terre, Haute Resolution visible (SPOT/HRV) systems are described and their limitations discussed. The questionable stability of in-flight absolute calibration methods suggests the use of a radiative transfer program to predict the apparent radiance, at the entrance pupil of the sensor, of a ground site of measured reflectance imaged through a well characterized atmosphere. The uncertainties of such a method are discussed.

Slater, P. N.↗
DOE OSTI2015

Influence of single particle orbital sets and configuration selection on multideterminant wavefunctions in quantum Monte Carlo

Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the application of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Theoretical study of a screened Hartree–Fock exchange potential using position-dependent atomic dielectric constants

Dielectric-dependent screened Hartree–Fock (HF) exchange potential and Slater-formula have been reported, where the ratio of the HF exchange term mixed into potentials is inversely proportional to the dielectric constant of the target semiconductor. This study introduces a position-dependent dielectric constant method in which the dielectric constant is partitioned between the atoms in a semiconductor. These partitioned values differ depending on the electrostatic environment surrounding the atoms and lead to position-dependent atomic dielectric constants. These atomic dielectric constants provide atomic orbital-based matrix elements for the screened exchange potentials. Energy band structures of several semiconductors and insulators are also presented to validate this approach.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Sign Learning Kink-based (SiLK) Quantum Monte Carlo for molecular systems

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H{sub 2}O, N{sub 2}, and F{sub 2} molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Correlations in rare-earth transition-metal permanent magnets

It is investigated how electron-electron correlations affect the intrinsic properties of rare-earth transition-metal magnets. Focusing on orbital moment and anisotropy, we perform model calculations for 3d-4f alloys and density-functional theory (DFT) calculations for NdCo{sub 5}. On an independent-electron level, the use of a single Slater determinant with broken spin symmetry introduces Hund's rule correlations, which govern the behavior of rare-earth ions and of alloys described by the local spin density approximation (LSDA) and LSDA + U approximations to DFT. By contrast, rare-earth ions in intermetallics involve configuration interactions between two or more Slater determinants and lead to phenomena such as spin-charge distribution. Analyzing DFT as a Legendre transformation and using Bethe's crystal-field theory, we show that the corresponding density functionals are very different from familiar LSDA-type expressions and outline the effect of spin-charge separation on the magnetocrystalline anisotropy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Hyperspherical Slater determinant approach to few-body fractional quantum Hall states

In a recent study (Daily et al., 2015), a hyperspherical approach has been developed to study few-body fractional quantum Hall states. This method has been successfully applied to the exploration of few boson and fermion problems in the quantum Hall region, as well as the study of inter-Landau level collective excitations (Rittenhouse et al., 2016; Wooten et al., 2016). However, the hyperspherical method as it is normally implemented requires a subsidiary (anti-)symmetrization process, which limits its computational effectiveness. The present work overcomes these difficulties and extends the power of this method by implementing a representation of the hyperspherical many-body basis space in terms of Slater determinants of single particle eigenfunctions. A clear connection between the hyperspherical representation and the conventional single particle picture is presented, along with a compact operator representation of the theoretical framework. - Highlights: • A hyperspherical method has been implemented to study the quantum Hall effect. • The hyperspherical many-body basis space is represented with Slater determinants. • Example numerical studies of the 4- and 8-electron systems are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Numerical evaluation of two-center integrals over Slater type orbitals

Slater Type Orbitals (STOs) which one of the types of exponential type orbitals (ETOs) are used usually as basis functions in the multicenter molecular integrals to better understand physical and chemical properties of matter. In this work, we develop algorithms for two-center overlap and two-center two-electron hybrid and Coulomb integrals which are calculated with help of translation method for STOs and some auxiliary functions by V. Magnasco’s group. We use Mathematica programming language to produce algorithms for these calculations. Numerical results for some quantum numbers are presented in the tables. Consequently, we compare our obtained numerical results with the other known literature results and other details of evaluation method are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Electronic Structure and Properties of Berkelium Iodates

The reaction of 249 Bk(OH) 4 with iodate under hydrothermal conditions results in the formation of Bk(IO 3 ) 3 as the major product with trace amounts of Bk(IO 3 ) 4 also crystallizing from the reaction mixture. The structure of Bk(IO 3 ) 3 consists of nine-coordinate Bk III cations that are bridged by iodate anions to yield layers that are isomorphous with those found for Am III , Cf III , and with lanthanides that possess similar ionic radii. Bk(IO 3 ) 4 was expected to adopt the same structure as M(IO 3 ) 4 (M = Ce, Np, Pu), but instead parallels the structural chemistry of the smaller Zr IV cation. Bk III –O and Bk IV –O bond lengths are shorter than anticipated and provide further support for a postcurium break in the actinide series. Photoluminescence and absorption spectra collected from single crystals of Bk(IO 3 ) 4 show evidence for doping with Bk III in these crystals. In addition to luminescence from Bk III in the Bk(IO 3 ) 4 crystals, a broad-band absorption feature is initially present that is similar to features observed in systems with intervalence charge transfer. However, the high-specific activity of 249 Bk ( t 1/2 = 320 d) causes oxidation of Bk III and only Bk IV is present after a few days with concomitant loss of both the BkIII luminescence and the broadband feature. The electronic structure of Bk(IO 3 ) 3 and Bk(IO 3 ) 4 were examined using a range of computational methods that include density functional theory both on clusters and on periodic structures, relativistic ab initio wave function calculations that incorporate spin–orbit coupling (CASSCF), and by a full-model Hamiltonian with spin–orbit coupling and Slater–Condon parameters (CONDON). Some of these methods provide evidence for an asymmetric ground state present in Bk IV that does not strictly adhere to Russel–Saunders coupling and Hund’s Rule even though it possesses a half-filled 5 f 7 shell. Multiple factors contribute to the asymmetry that include 5 f electrons being present in microstates that are not solely spin up, spin–orbit coupling induced mixing of low-lying excited states with the ground state, and covalency in the Bk IV –O bonds that distributes the 5f electrons onto the ligands. These factors are absent or diminished in other f 7 ions such as Gd III or Cm III .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Condensed phase QM/MM simulations utilizing the exchange core functions to describe exchange repulsions at the QM boundary region

In a recent work, we developed a method [H. Takahashi et al., J. Chem. Phys. 143, 084104 (2015)] referred to as exchange-core function (ECF) approach, to compute exchange repulsion E{sub ex} between solute and solvent in the framework of the quantum mechanical (QM)/molecular mechanical (MM) method. The ECF, represented with a Slater function, plays an essential role in determining E{sub ex} on the basis of the overlap model. In the work of Takahashi et al. [J. Chem. Phys. 143, 084104 (2015)], it was demonstrated that our approach is successful in computing the hydrogen bond energies of minimal QM/MM systems including a cationic QM solute. We provide in this paper the extension of the ECF approach to the free energy calculation in condensed phase QM/MM systems by combining the ECF and the QM/MM-ER approach [H. Takahashi et al., J. Chem. Phys. 121, 3989 (2004)]. By virtue of the theory of solutions in energy representation, the free energy contribution δμ{sub ex} from the exchange repulsion was naturally formulated. We found that the ECF approach in combination with QM/MM-ER gives a substantial improvement on the calculation of the hydration free energy of a hydronium ion. This can be attributed to the fact that the ECF reasonably realizes the contraction of the electron density of the cation due to the deficit of an electron.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1984

Spectroradiometric calibration of the Thematic Mapper and Multispectral Scanner system

The newly built Caste spectropolarimeters gave satisfactory performance during tests in the solar radiometer and helicopter modes. A bandwidth normalization technique based on analysis of the moments of the spectral responsivity curves was used to analyze the spectral bands of the MSS and TM subsystems of LANDSAT 4 and 5 satellites. Results include the effective wavelength, the bandpass, the wavelength limits, and the normalized responsivity for each spectral channel. Temperature coefficients for TM PF channel 6 were also derived. The moments normalization method used yields sensor parameters whose derivation is independent of source characteristics (i.e., incident solar spectral irradiance, atmospheric transmittance, or ground reflectance). The errors expected using these parameters are lower than those expected using other normalization methods.

Palmer, J. M.↗
DOE OSTI2026

Fermionic mean-field dynamics for spin systems beyond free fermions

We introduce the fermionized time-dependent Hartree–Fock (fTDHF), a real-time quantum dynamics method for spin-1/2 Hamiltonians following their mapping to fermions via the Jordan-Wigner transformation. fTDHF is formally equivalent to exact dynamics in the case of free fermions, and can efficiently handle non-local string operators arising from long-range interactions via transition matrix elements between non-orthogonal Slater determinants. We show that the fTDHF method can be implemented on a classical computer with a cost that scales polynomially with system size, and linearly with the time steps. We benchmark fTDHF against exact dynamics on three separate spin-1/2 models, representing adiabatic preparation of states with long-range correlations, disorder-driven observation of many-body localization, and particle production in the Schwinger model. For each of these systems, fTDHF is shown to reproduce the qualitative dynamics generated by the exact evolutions, while maintaining a simple physical picture due to its mean-field nature.

Dutta, Rishab↗
DOE OSTI2020

Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced. This approach is illustrated in the case of the carbon diamond using Slater–Jastrow trial wavefunctions including up to one million Slater determinants. Fixed-node DMC energies obtained with such large expansions are much improved, and the fixed-node error is found to decrease monotonically and smoothly as a function of the number of determinants in the trial wavefunction, a property opening the way to a better control of this error. The cohesive energy extrapolated to the thermodynamic limit is in close agreement with the estimated experimental value. Interestingly, this is also the case at the single-determinant level, thus, indicating a very good error cancellation in carbon diamond between the bulk and atomic total fixed-node energies when using single-determinant nodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗