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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Neuralized fermionic tensor networks for quantum many-body systems

In this work, we describe a class of neuralized fermionic tensor network states (NN-fTNSs) that introduce nonlinearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction uses the fTNS algebra to implement a natural fermionic sign structure and is compatible with standard tensor network algorithms but gains enhanced expressivity through the neural network parametrization. Using the 1D and 2D Fermi-Hubbard models as benchmarks, we demonstrate that NN-fTNSs achieve order of magnitude improvements in the ground-state energy compared to pure fTNSs with the same bond dimension and can be systematically improved through both the tensor network bond dimension and the neural network parametrization. Compared to existing fermionic neural quantum states based on Slater determinants and Pfaffians, NN-fTNSs offer a physically motivated alternative fermionic structure. Furthermore, compared to such states, NN-fTNSs naturally exhibit improved computational scaling and we demonstrate a construction that achieves linear scaling with the lattice size.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Fokker-Planck Equation Governing the Distribution of Walkers in Auxiliary-Field Quantum Monte Carlo

Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying Fokker-Planck equation governing the walker population distribution has remained unknown. Here, in this Letter, we derive the Fokker-Planck equation for AFQMC and propose a novel numerical scheme to solve it. The solution of the Fokker-Planck equation reveals the wave function actually sampled by the AFQMC algorithm. Interestingly, we find that even when the exact ground state is used as a guiding wave function in constrained path AFQMC, contrary to the common assumption, the wave function sampled by AFQMC is not exact. Beyond clarifying several fundamental aspects of AFQMC, the availability of a Fokker-Planck equation formulation opens new avenues for systematically improving its accuracy, which we outline in this Letter.

Monte Carlo methods↗
NASA NTRS1982

Integral dependent spin couplings in CI calculations

Although the number of ways to combine Slater determinants to form spin eigenfunctions increases rapidly with the number of open shells, most of these spin couplings will make only a small contribution to a given state, provided the spin coupling is chosen judiciously. The technique of limiting calculations to the interacting subspace pioneered by Bunge (1970) was employed by Munch and Davidson (1975) to the vanadium atom. The use of an interacting space looses its advantage in more complex cases. However, the problem can always be reduced to only one interacting spin coupling by making the coefficients integral dependent. The present investigation is concerned with the performance of integral dependent interacting couplings, taking into account the results of three test calculations.

Iberle, K.↗
DOE OSTI2022

The binding of atomic hydrogen on graphene from density functional theory and diffusion Monte Carlo calculations

In this research, density functional theory (DFT) and diffusion Monte Carlo (DMC) methods are used to calculate the binding energy of a H atom chemisorbed on the graphene surface. The DMC value of the binding energy is about 16% smaller in magnitude than the Perdew–Burke–Ernzerhof (PBE) result. The inclusion of exact exchange through the use of the Heyd–Scuseria–Ernzerhof functional brings the DFT value of the binding energy closer in line with the DMC result. It is also found that there are significant differences in the charge distributions determined using PBE and DMC approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Thermal mean-field theories

Several closely related ab initio thermal mean-field theories for fermions, both well-established and new ones, are compared with one another at the formalism level and numerically. The theories considered are Fermi–Dirac theory; thermal Hartree–Fock (HF) theory; two modifications of the thermal single-determinant and the first-order finite-temperature many-body perturbation theory based on a zero-temperature or thermal HF reference. Furthermore, thermal full-configuration-interaction theory is used as the benchmark.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Piecewise interaction picture density matrix quantum Monte Carlo

The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact N-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC (IP-DMQMC) method that overcomes the limitation of only sampling one inverse temperature point at a time, instead allowing for the sampling of a temperature range within a single calculation, thereby reducing the computational cost. At the target inverse temperature, instead of ending the simulation, we incorporate a change of picture away from the interaction picture. The resulting equations of motion have piecewise functions and use the interaction picture in the first phase of a simulation, followed by the application of the Bloch equation once the target inverse temperature is reached. We find that the performance of this method is similar to or better than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.

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

The exact exchange–correlation potential in time-dependent density functional theory: Choreographing electrons with steps and peaks

The time-dependent exchange–correlation potential has the unusual task of directing fictitious non-interacting electrons to move with exactly the same probability density as true interacting electrons. This has intriguing implications for its structure, especially in the non-perturbative regime, leading to step and peak features that cannot be captured by bootstrapping any ground-state functional approximation. Here, we review what has been learned about these features in the exact exchange–correlation potential of time-dependent density functional theory in the past decade or so and implications for the performance of simulations when electrons are driven far from any ground state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Sub-system self-consistency in coupled cluster theory

Here, in this article, we provide numerical evidence indicating that the single-reference coupled-cluster (CC) energies can be calculated alternatively to their copybook definition. We demonstrate that the CC energy can be reconstructed by diagonalizing the effective Hamiltonians describing correlated sub-systems of the many-body system. In the extreme case, we provide numerical evidence that the CC energy can be reproduced through the diagonalization of the effective Hamiltonian describing sub-system composed of a single electron. These properties of the CC formalism can be exploited to design protocols to define effective interactions in sub-systems used as probes to calculate the energy of the entire system and introduce a new type of self-consistency for approximate CC approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Downward quantum learning from element 118: Automated generation of Fermi–Löwdin orbitals for all atoms

A new algorithm based on a rigorous theorem and quantum data computationally mined from element 118 guarantees automated construction of initial Fermi–Löwdin-Orbital (FLO) starting points for all elements in the Periodic Table. It defines a means for constructing a small library of scalable FLOs for universal use in molecular and solid-state calculations. The method can be systematically improved for greater efficiency and for applications to excited states such as x-ray excitations and optically silent excitations. FLOs were introduced to recast the Perdew–Zunger self-interaction correction (PZSIC) into an explicit unitarily invariant form. The FLOs are generated from a set of N quasi-classical electron positions, referred to as Fermi-Orbital descriptors (FODs), and a set of N-orthonormal single-electron orbitals. FOD positions, when optimized, minimize the PZSIC total energy. However, creating sets of starting FODs that lead to a positive definite Fermi orbital overlap matrix has proven to be challenging for systems composed of open-shell atoms and ions. The proof herein guarantees the existence of a FLOSIC solution and further guarantees that if a solution for N electrons is found, it can be used to generate a minimum of N – 1 and a maximum of 2 N – 2 initial starting points for systems composed of a smaller number of electrons. As a result, applications to heavy and super-heavy atoms are presented. All starting solutions reported here were obtained from a solution for element 118, Oganesson.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

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

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

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Kohn–Sham Density in a Slater Orbital Basis Set

Finite, atom-centered Slater basis sets are used to determine approximate Kohn–Sham molecular orbitals. This is achieved by minimizing the kinetic energy plus the sum-squared difference between the Kohn–Sham density and the full configuration interaction density. As a result of the finite basis, a weight factor is introduced to balance the two minimization components. Results herein show that this can be done systematically, without sensitive dependence on the choice of scaling factor. In addition, the algorithm is applied to the LiH diatomic for fractional electron counts, where stretching the bond introduces significant reorganization of the electron density. As a result, the analysis will show the correct KS orbital structure and reveal the effects of correlation and electron locality on the KS solutions.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1968

Electronic wave functions for atoms. I.

Atomic wave functions determination by configuration interaction method, constructing Slater type orbitals into orthogonal set of smaller dimensions

Bunge, C. F.↗
NASA NTRS1972

Apollo 9 multiband photography experiment S065

Fourier analysis was applied to microdensitometer scans of a selected region of one SO65 frame in each of the three black-and-white bands. The approach was unique because a somewhat arbitrary section of the image was used and not limited to available targets as in edge analysis. Comparison of duplicates and calculation of absolute SO65 MTF were done by applying linear systems theory to the spatial spectra of the image scans. It was found that the duplication process was nonlinear and resulted in general amplification of spatial frequency modulation. However, the increase in modulation was offset by a corresponding increase in the granularity of the copies. The amount of increase seemed to be related to the initial granularity, but a direct relationship was not verified. Band-to-band comparison of image quality was achieved in the form of signal-to-noise ratio curves as a function of spatial frequency for each band. From this standpoint the DD band was an order of magnitude better than the other two. These were several factors that restricted the analysis of the Apollo 9 imagery. Among these were the lack of precise sensitometric and optical system data on the high altitude photography. In addition it was determined that there was only one simultaneous pair of high altitude and SO65 frames. Finally, the original SO65 photography was not available for scanning (for obvious reasons), thus eliminating a reference base for granularity and SO65 MTF determination.

Schowengerdt, R. A.↗
NASA NTRS1986

Exact formulas for multipole moments using Slater-type molecular orbitals

A triple infinite sum of formulas expressed as an expansion in Legendre polynomials is generated by use of computer algebra to represent the potential from the midpoint of two Slater-type orbitals; the charge density that determines the potential is given as the product of the two orbitals. An example using 1s orbitals shows that only a few terms are needed to obtain four-figure accuracy. Exact formulas are obtained for multipole moments by means of a careful study of expanded formulas, allowing an 'extrapolation to infinity'. This Loewdin alpha-function approach augmented by using a C matrix to characterize Slater-type orbitals can be readily generalized to all cases.

Jones, H. W.↗
NASA NTRS1967

Confirmation of the predicted Hartree-Fock limit in BeH sub 2.

We have recently estimated the total energy of the BeH 2 molecule as -15.918 ± 0.015 au. One of the steps in the analysis was to estimate the difference between the SCF energies computed with a minimal basis set of Slater orbits and with the best possible single-determinant wave function, the so-called Hartree-Fock limit and was predicted to be -15.773 ± 0.007 au for BeH 2 .

Molecular energy↗
NASA NTRS1980

MRS proof-of-concept on atmospheric corrections. Atmospheric corrections using an orbital pointable imaging system

The feasibility of using a pointable imager to determine atmospheric parameters was studied. In particular the determination of the atmospheric extinction coefficient and the path radiance, the two quantities that have to be known in order to correct spectral signatures for atmospheric effects, was simulated. The study included the consideration of the geometry of ground irradiance and observation conditions for a pointable imager in a LANDSAT orbit as a function of time of year. A simulation study was conducted on the sensitivity of scene classification accuracy to changes in atmospheric condition. A two wavelength and a nonlinear regression method for determining the required atmospheric parameters were investigated. The results indicate the feasibility of using a pointable imaging system (1) for the determination of the atmospheric parameters required to improve classification accuracies in urban-rural transition zones and to apply in studies of bi-directional reflectance distribution function data and polarization effects; and (2) for the determination of the spectral reflectances of ground features.

Slater, P. N.↗
NASA NTRS1978

Theoretical study of HSiO/+/ and HOSi/+/

Results are reported for quantum-mechanical studies of the ions HSiO(+) and HOSi(+). The equilibrium geometries, rotation constants, and relative stabilities of these ions are determined using the matrix Hartree-Fock model with a basis set of Slater exponential functions. Optimum bond lengths are calculated, and an empirical correction to the computed bond lengths is introduced. The isomer HOSi(+) is found to be more stable than HSiO(+). A frequency of 35.77 GHz is obtained for the J = 1-0 transition of HOSi(+) by assuming that the vibration-rotation interaction constants for this isomer are the same as those for HCP.

Wilson, S.↗