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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.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Proper orthogonal descriptors for efficient and accurate interatomic potentials

Here, we present the proper orthogonal descriptors for efficient and accuracy representation of the potential energy surface. The potential energy surface is represented as a many-body expansion of parametrized potentials in which the potentials are functions of atom positions and parameters. The proper orthogonal decomposition is employed to decompose the parametrized potentials into a set of proper orthogonal descriptors (PODs). Because of the rapid convergence of the proper orthogonal decomposition, relevant snapshots can be sampled exhaustively to represent the atomic neighborhood environment accurately with a small number of descriptors. The proper orthogonal descriptors are used to develop interatomic potentials by using a linear expansion of the descriptors and determining the expansion coefficients from a weighted least-squares regression against a density functional theory (DFT) training set. We present a comprehensive evaluation of the POD potentials on previously published DFT data sets comprising Li, Mo, Cu, Ni, Si, Ge, and Ta elements. The data sets represent a diverse pool of metals, transition metals, and semiconductors. The accuracy of the POD potentials are comparable to that of state-of-the-art machine learning potentials such as the spectral neighbor analysis potential (SNAP) and the atomic cluster expansion (ACE).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Quick-and-Easy Validation of Protein–Ligand Binding Models Using Fragment-Based Semiempirical Quantum Chemistry

Electronic structure calculations in enzymes converge very slowly with respect to the size of the model region that is described using quantum mechanics (QM), requiring hundreds of atoms to obtain converged results and exhibiting substantial sensitivity (at least in smaller models) to which amino acids are included in the QM region. As such, there is considerable interest in developing automated procedures to construct a QM model region based on well-defined criteria. However, testing such procedures is burdensome due to the cost of large-scale electronic structure calculations. Here, we show that semiempirical methods can be used as alternatives to density functional theory (DFT) to assess convergence in sequences of models generated by various automated protocols. The cost of these convergence tests is reduced even further by means of a many-body expansion. We use this approach to examine convergence (with respect to model size) of protein–ligand binding energies. Fragment-based semiempirical calculations afford well-converged interaction energies in a tiny fraction of the cost required for DFT calculations. Two-body interactions between the ligand and single-residue amino acid fragments afford a low-cost way to construct a “QM-informed” enzyme model of reduced size, furnishing an automatable active-site model-building procedure. This provides a streamlined, user-friendly approach for constructing ligand binding-site models that needs neither a priori information nor manual adjustments. Extension to model-building for thermochemical calculations should be straightforward.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Convergent Protocols for Computing Protein–Ligand Interaction Energies Using Fragment-Based Quantum Chemistry

Fragment-based quantum chemistry methods offer a way to sidestep the steep nonlinear scaling of electronic structure calculations so that large molecular systems can be investigated using high-level methods. Here, we use fragmentation to compute protein–ligand interaction energies in systems with several thousand atoms, using a new software platform for managing fragment-based calculations that implements a screened many-body expansion. Convergence tests using a minimal-basis semiempirical method (HF-3c) indicate that two-body calculations, with single-residue fragments and simple hydrogen caps, are sufficient to reproduce interaction energies obtained using conventional supramolecular electronic structure calculations, to within 1 kcal/mol at about 1% of the computational cost. We also demonstrate that the HF-3c results are illustrative of trends obtained with density functional theory in basis sets up to augmented quadruple-ζ quality. Strategic deployment of fragmentation facilitates the use of converged biomolecular model systems alongside high-quality electronic structure methods and basis sets, bringing ab initio quantum chemistry to systems of hitherto unimaginable size. This will be useful for generation of high-quality training data for machine learning applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Toward Full Configuration Interaction for Transition-Metal Complexes

In this work, an efficacious approximation to full configuration interaction (FCI) is adapted to calculate singlet-triplet gaps for transition-metal complexes. This strategy, incremental FCI (iFCI), uses a many-body expansion to systematically add correlation to a simple reference wave function and therefore achieves greatly reduced computational costs compared to FCI. iFCI through the 3-body expansion is demonstrated on four model transition-metal complexes involving the metals Zn, V, and Cu. Screening techniques to increase the computational efficiency of iFCI are proposed and tested, showing reduction in the number of 3-body terms by more than 90% with controlled errors. The largest complex treated by iFCI has 142 valence electrons, all of which are correlated among the full set of 444 active orbitals. Computed spin gaps approach experimental results for the four complexes, though room for improvement remains.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Coupled Cluster Downfolding Methods: the effect of double commutator terms on the accuracy of ground-state energies

Downfolding coupled cluster (CC) techniques have recently been introduced into quantum chemistry as a tool for the dimensionality reduction of the many-body quantum problem. As opposed to earlier formulations in physics and chemistry based on the concept of effective Hamiltonians, the appearance of the downfolded Hamiltonians is a natural consequence of the single-reference exponential parametrization of the wave function. In this paper, we discuss the impact of higher-order terms originating in double commutators. In analogy to previous studies, we consider the case when only one- and two-body interactions are included in the downfolded Hamiltonians. We demonstrate the efficiency of the many-body expansions involving single and double commutators for the unitary extension of the downfolded Hamiltonians on the example of the beryllium atom, and bond-breaking processes in the Li2 and H2O molecules. For the H2O system, we also analyze energies obtained with downfolding procedures as functions of the active space size.

quantum computing, quantum algorithms, electronic ↗
DOE OSTI2023

Data efficiency and extrapolation trends in neural network interatomic potentials

Abstract Recently, key architectural advances have been proposed for neural network interatomic potentials (NNIPs), such as incorporating message-passing networks, equivariance, or many-body expansion terms. Although modern NNIP models exhibit small differences in test accuracy, this metric is still considered the main target when developing new NNIP architectures. In this work, we show how architectural and optimization choices influence the generalization of NNIPs, revealing trends in molecular dynamics (MD) stability, data efficiency, and loss landscapes. Using the 3BPA dataset, we uncover trends in NNIP errors and robustness to noise, showing these metrics are insufficient to predict MD stability in the high-accuracy regime. With a large-scale study on NequIP, MACE, and their optimizers, we show that our metric of loss entropy predicts out-of-distribution error and data efficiency despite being computed only on the training set. This work provides a deep learning justification for probing extrapolation and can inform the development of next-generation NNIPs.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A Systematic, Polynomial-Cost Approach to Exact Correlation Energies (Final Technical Report)

The full configuration interaction (FCI) wave function provides the exact solution to the Schrödinger equation in a given basis set. While FCI is intractable due to exponential computational costs, the many-body expansion (or the method of increments) can reduce scaling to a low-order polynomial with system size. This project entailed advances in the incremental FCI (iFCI) approach, designed to allow iFCI to reach larger system sizes and maintain its intrinsic high accuracy. This document describes advances in solvers for iFCI, strategies to treat multiple charge and spin states, and virtual state management methods to reduce memory requirements. Overall, this project allows iFCI to correlate (for the first time) 142 valence electrons in 444 orbitals in a realistic model of a transition metal complex.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Exact two-body expansion of the many-particle wave function

Progress toward the solution of the strongly correlated electron problem has been stymied by the exponential complexity of the wave function. Previous work established an exact two-body exponential product expansion for the ground-state wave function. By developing a reduced density-matrix analog of Dalgarno-Lewis perturbation theory, we prove here that (i) the two-body exponential product expansion is rapidly and globally convergent with each operator representing an order of a renormalized perturbation theory, (ii) the energy of the expansion converges quadratically near the solution, and (iii) the expansion is exact for both ground and excited states. The two-body expansion offers a reduced parametrization of the many-particle wave function as well as the two-particle reduced density matrix with potential applications on both conventional and quantum computers for the study of strongly correlated quantum systems. In this work, we demonstrate the result with the exact solution of the contracted Schrödinger equation for the molecular chains H 4 and H 5 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

ADG: automated generation and evaluation of many-body diagrams

The goal of the present paper is twofold. First, a novel expansion many-body method applicable to superfluid open-shell nuclei, the so-called Bogoliubov in-medium similarity renormalization group (BIMSRG) theory, is formulated. This generalization of standard single-reference IMSRG theory for closed-shell systems parallels the recent extensions of coupled cluster, self-consistent Green’s function or many-body perturbation theory. Within the realm of IMSRG theories, BIMSRG provides an interesting alternative to the already existing multi-reference IMSRG (MR-IMSRG) method applicable to open-shell nuclei. The algebraic equations for low-order approximations, i.e., BIMSRG(1) and BIMSRG(2), can be derived manually without much difficulty. However, such a methodology becomes already impractical and error prone for the derivation of the BIMSRG(3) equations, which are eventually needed to reach high accuracy. Based on a diagrammatic formulation of BIMSRG theory, the second objective of the present paper is thus to describe the third version (v3.0) of the code that automatically (1) generates all valid BIMSRG(n) diagrams and (2) evaluates their algebraic expressions in a matter of seconds. This is achieved in such a way that equations can easily be retrieved for both the flow equation and the Magnus expansion formulations of BIMSRG. Expanding on this work, the first future objective is to numerically implement BIMSRG(2) (eventually BIMSRG(3)) equations and perform ab initio calculations of mid-mass open-shell nuclei.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1977

Diagrammatic perturbation theory - The ground state of the carbon monosulfide molecule

Diagrammatic many-body perturbation theory is employed in a study of the ground state of the carbon monosulfide molecule for bond lengths close to the equilibrium value. The calculations are complete through third order in the energy within the algebraic approximation. Two different zero-order Hamiltonians are considered, and all two-, three-, and four-body terms are determined for the corresponding perturbation expansions. Many-body effects are found to be very important. Pade approximants to the energy expansion are constructed, and upper bounds evaluated. Almost 53 percent of the estimated correlation energy is recovered. The variation of components of the correlation energy with nuclear separation is investigated. Spectroscopic constants are also calculated.

Wilson, S.↗
DOE OSTI2023

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick’s theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Fragme∩t: An Open‐Source Framework for Multiscale Quantum Chemistry Based on Fragmentation

Fragment-based quantum chemistry offers a means to circumvent the nonlinear computational scaling of conventional electronic structure calculations, by partitioning a large calculation into smaller subsystems then considering the many-body interactions between them. Variants of this approach have been used to parameterize classical force fields and machine learning potentials, applications that benefit from interoperability between quantum chemistry codes. However, there is a dearth of software that provides interoperability yet is purpose-built to handle the combinatorial complexity of fragment-based calculations. To fill this void we introduce “Fragme∩t”, an open-source software application that provides a tool for community validation of fragment-based methods, a platform for developing new approximations, and a framework for analyzing many-body interactions. Fragme∩t includes algorithms for automatic fragment generation and structure modification, and for distance- and energy-based screening of the requisite subsystems. Checkpointing, database management, and parallelization are handled internally and results are archived in a portable database. Interfaces to various quantum chemistry engines are easy to write and exist already for Q-Chem, PySCF, xTB, Orca, CP2K, MRCC, Psi4, NWChem, GAMESS, and MOPAC. Applications reported here demonstrate parallel efficiencies around 96% on more than 1000 processors but also showcase that the code can handle large-scale protein fragmentation using only workstation hardware, all with a codebase that is designed to be usable by non-experts. Fragme∩t conforms to modern software engineering best practices and is built upon well established technologies including Python, SQLite, and Ray. The source code is available under the Apache 2.0 license.

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

Interpretable, extensible linear and symbolic regression models for charge density prediction using a hierarchy of many-body correlation descriptors

Here, density functional theory (DFT) is routinely used to make electronic structure predictions for high-throughput screening of materials and molecules for technologically relevant areas, like the identification of better catalysts, electronic materials, and drug discovery. However, the DFT formalism is limited by (a) its poor (quadratic-to-quartic) scaling, and (b) the need to perform repeated eigenvalue computations of the electronic Hamiltonian as part of its self-consistent field (SCF) iteration procedure to obtain the converged ground state electron density, ρ (r). Approaches that directly predict ρ (r) of a structure with high accuracy can accelerate conventional SCF calculations and can also be used in linearly scaling methods such as orbital-free DFT. To this end, we present a procedure to predict the ground state electron density of molecular and periodic three-dimensional systems directly from the atomic structure with a particular emphasis on physical interpretability. In our framework, ρ (r) is modeled using many-body correlation descriptors that accurately capture the effects of local atomic arrangements in the neighborhood of a grid point. Our use of a linear regression scheme to fit to charge density data enables transparent analysis of the relative contributions of various types of local atomic correlations. By systematically including increasingly complex correlations, our model is shown to accurately predict ρ (r) for a variety of chemically and electronically diverse systems — amorphous Ge, Al(001) slab, crystalline Ga 2 O 3 , molecular benzene, and polyethylene. We then demonstrate a symbolic regression-based protocol to construct easily computable, interpretable features from lower-order correlations that significantly improves our electron density predictions with effectively no increase in the computational cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Performance of wave function and Green's function methods for non-equilibrium many-body dynamics

Theoretical descriptions of the non-equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on the truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non-equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single-particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for a critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity-transformed Hamiltonians (coupled-cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single-particle density matrix. The dynamics predicted by Green's functions in the (widely popular) G W approximation are less accurate, but improve significantly upon the mean-field results in the strongly driven regime. Published by the American Physical Society 2025

Reeves, Cian C. (ORCID:0009000642581845)↗
NASA NTRS1975

Many-body-theory study of lithium photoionization

A detailed theoretical calculation is carried out for the photoionization of lithium at low energies within the framework of Brueckner-Goldstone perturbational approach. In this calculation extensive use is made of the recently developed multiple-basis-set technique. Through this technique all second-order perturbation terms, plus a number of important classes of terms to infinite order, have been taken into account. Analysis of the results enables one to resolve the discrepancies between two previous works on this subject. The detailed calculation also serves as a test on the convergence of the many-body perturbation-expansion approach.

Chang, T. N.↗
DOE OSTI2021

A systematic analysis of phase stability in refractory high entropy alloys utilizing linear and non-linear cluster expansion models

We report that obtaining surrogate models for various types of materials has long been a goal of computational material scientists and physicists, as they allow the calculation of thermodynamic quantities and properties of interest far more efficiently than DFT. Many surrogate models, including interatomic potentials generated by machine learning algorthims and cluster expansions, rely on incorporating many-body interactions such as three-body or four-body interactions. When utilizing machine learning algorithms for interatomic potentials, it is common to start with two-body interactions and systematically include three- and four-body clusters to improve the fit, stopping when including the additional clusters does not measurably change the predictive power of the model. In cluster expansions for FCC and related lattices, it is often enough to include mostly two-body interactions and a handful of three-body interactions. However, it remains to be seen whether those will be enough in the case of lattices with a lower packing fraction, such as BCC.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Exact block encoding of imaginary time evolution with universal quantum neural networks

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.

97 MATHEMATICS AND COMPUTING↗