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32 records · Page 2
All sourcesNASA NTRSDOE OSTI
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↗
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

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↗
DOE OSTI2022

Quantification of electron correlation for approximate quantum calculations

State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater–Jastrow wave functions.

Chemistry↗
DOE OSTI2025

Kβ X-ray Emission Spectra Analysis Using Bayesian Optimization

The Kβ X-ray emission spectrum of 3 d transition metals is rich with electronic and structural information due to strong exchange interactions with the valence shell of the metal, and has become crucial for understanding their spin and oxidation states. The spectrum is commonly treated using crystal-field multiplet theory, a semi-empirical theory that uses tunable parameters to control the strength of the effects present in X-ray emission spectroscopy (XES). However, determining the experimental values of these parameters remains a challenge. We present a methodology that applies Bayesian optimization to crystal-field multiplet theory to determine parameter values. The algorithm is tested on the X-ray emission spectra of a collection of Mn, Co, and Ni oxides. We are able to find optimal values for the four most impactful parameters: Slater−Condon reduction factors F dd , F pd , and G pd , and crystal field splitting 10 Dq . The algorithm produces significantly improved accuracy compared to current analysis methods, and probes interparameter dependencies by modeling the error landscape. This advancement enhances XES analysis by offering an approach of obtaining quantitative electronic structural information on 3 d transition metal valence shells, facilitating applications across various scientific fields.

Bayesian optimization↗
DOE OSTI2025

Evaluating opportunity for distributed wind energy in rural and agricultural areas

Wind energy is among the most mature renewable energy technologies, accounting for 11% of the current US electricity generation in 2024, with the lowest average levelized cost. While it is known that substantial opportunity exists for further development, a key question has been where wind energy is best suited compared to other technologies. This study leverages an immense dataset of parcel-resolved technoeconomic potential for the contiguous United States, focusing on distributed wind (DW) energy—a configuration where one or more turbines, typically 30–60 m in height are used to satisfy nearby energy needs. The analysis is conducted at multiple spatial scales and considers land use, crop land, census, and incentive program data to determine the most opportune areas for market development. The results show that rural, agricultural and residential areas are most suited to DW. Connection type (in front of, or behind the meter) and regulations determine the best application, while siting constraints, economics, demand and the wind resource determines the optimal size of turbine.

17 WIND ENERGY↗
DOE OSTI2024

Exploring limitations in the induced polarization versus surface conductivity relationship in the case of wetland soils

Recent induced polarization studies suggest that the real part of surface conductivity (σ' surf ) scales linearly with the imaginary conductivity (σ'' = σ'' surf ) or normalized chargeability (Mn) for a range of soil types. The coefficients of this relationship l and l_Mn ( l = σ''/σ' surf or l_Mn = Mn/σ' surf ) allow the separation of the surface and electrolytic conductivities from the bulk conductivity. However, the dependence of these constants on varying soil physicochemical properties, including under unsaturated conditions, is yet to be assessed. Using estimates of σ' surf from 18 undisturbed soil samples from a restored wetland and σ'' measured over a frequency range of 0.01 Hz to 10 kHz, the σ' surf and σ'' were compared with the laboratory measurements of soil properties. Also, l and l_Mn were calculated for each soil sample and regressed them against the soil properties. We find an apparent dependence of l on soil texture, bulk density, organic matter, and moisture contents, with coefficients of determination (R 2 ) ranging from 0.5 to 0.65 at low frequencies (e.g., 1 Hz) but not at high frequencies (e.g., 936 Hz). This dependence of l on soil texture results from the insensitivity of σ'' at low frequency to σ' surf and, by implication, to the soil properties controlling σ' surf . In contrast, l_Mn indicates no correlation with the soil properties because Mn is linearly correlated with σ' surf and correlated with the soil properties controlling σ' surf . Finally, our results call for caution on the application of σ'' at a single frequency as a proxy of σ' surf because σ'' is not necessarily correlated with σ' surf across all soil types. Although using l_Mn derived from multifrequency measurements overcomes this limitation, field acquisition of spectral information (e.g., up to 1000 Hz) remains a challenge.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Spectral induced polarization (SIP) measurements across a PFAS-contaminated source zone

There is a pressing need for the development of field-scale, in situ screening technologies for assessing variations in aqueous film forming foam (AFFF) concentrations in soils at former fire training and storage sites. Field-scale Spectral Induced Polarization (SIP) geophysical measurements were acquired on a transect crossing an AFFF source zone. Soil samples were acquired from ten locations and used to determine variations in poly- and per-fluoroalkyl substances (PFAS) concentrations in soils and soil texture. These samples were also used to create triplicate soil columns for laboratory-grade SIP measurements. Field and laboratory observations provide evidence that SIP measurements are sensitive to the concentration of AFFF constituents associated with the pore surface in soils. The phase of the SIP measurements on the laboratory samples was linearly correlated with total soil-sorbed PFAS concentration. The phase from the field SIP measurements was highest over the location of maximum PFAS concentration measured on the laboratory samples, although a significant correlation between field-measured phase and laboratory-measured total PFAS concentration was not established. The sensitivity of the SIP response to the removal of soil PFAS using a methanol wash procedure (total PFAS concentration drop of 366 ppb) adds evidence for the case for SIP characterization of AFFF source zones. The results of these studies suggest that SIP might be developed into a field-scale technology for rapid, indirect assessment of AFFF source zones. Such a technology could improve the effectiveness of AFFF source zone characterization at reduced costs.

58 GEOSCIENCES↗
DOE OSTI2024

Investigating Soil Organic Matter Complexation using Spectral Induced Polarization

Spectral induced polarization (SIP) laboratory experiments were conducted to determine the sensitivity of this method to the formation of soil organic matter (SOM) complexes, with a long-term goal of field-scale monitoring. There are few SIP experiments that have explored this topic, yet understanding the dynamic behavior and interactions of SOM at the field scale could provide insight into soil fertility and health which influences crop yields, microorganisms that degrade organic pollutants, and carbon stabilization. We present the results of three experiments where the iron oxide, ferrihydrite (Fhy), was used to coat different media, and then the OM compound pentaglycine (PG) was pulse injected to form SOM complexes. SIP data was collected during these injections to capture any surface complexation changes. These experiments were performed in 1) a fluidic cell containing a micromodel, 2) a column containing Fhy coated ceramic beads and 3) a column containing Fhy coated Accusand®. Our results show a higher frequency response (defined here as > 1 Hz) in all three experiments, with the largest amplitude response after the first PG injection (Figure S.1). The repeatability of this response is encouraging and supporting data collected on the Accusand® experiment provides preliminary insight into the mechanisms controlling the SIP signatures. Sampling of fluid conductivity $σ_w$ and pH may indicate deprotonation of SOM occurring or rapid adsorption and release of protons from the Fhy sites. However additional experiments are needed to identify and confirm the primary and secondary reactions impacting the SIP response. We are looking towards other opportunities to continue this work, particularly to repeat experiments while collecting supporting datasets.

58 GEOSCIENCES↗
DOE OSTI2026

Advected carbon younger than the sediment fuels microbial metabolism in a pumped deep aquifer

Ever deeper wells are drilled worldwide to pump potable groundwater. Recent studies argue that overpumping compresses clays and releases reactive dissolved organic carbon (DOC), which in turn drives a series of microbial reactions that affect groundwater potability including arsenic concentrations. Here, we use a novel method to measure the radiocarbon ages of microbial RNA to determine the source of reactive or metabolizable DOC and argue against the compression of clays as the sole source of carbon. We show that microbial RNA (5,230; 5,550; 6,250 yr; n = 3 wells), DOC (280-10,800 yr; n = 13), and methane (modern to 6,240 yr; n = 3), from an overpumped deep aquifer in Bangladesh are much younger than the overlying clay layers deposited during the Pleistocene over 12,000 years ago. Mass-balance indicates that at least half of the carbon incorporated into RNA has to come from reactive DOC or methane that is advected downward via vertical recharge. This metabolism of advected organic carbon could have implications for the quality of water pumped from deep aquifers.

Biological and medical sciences↗