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Results for “Hartree-Fock 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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Laser pulse induced second- and third-harmonic generation of gold nanorods with real-time time-dependent density functional tight binding (RT-TDDFTB) method

In this paper, we investigate second- and third-harmonic generation processes in Au nanorod systems using the real-time time-dependent density functional tight binding method. Our study focuses on the computation of nonlinear signals based on the time dependent dipole response induced by linearly polarized laser pulses interacting with nanoparticles. We systematically explore the influence of various laser parameters, including pump intensity, duration, frequency, and polarization directions, on harmonic generation. We demonstrate all the results using Au nanorod dimer systems arranged in end-to-end configurations, and disrupting the spatial symmetry of regular single nanorod systems is crucial for second-harmonic generation processes. Furthermore, we study the impact of nanorod lengths, which lead to variable plasmon energies, on harmonic generation, and estimates of polarizabilities and hyper-polarizabilities are provided.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Scalable learning of potentials to predict time-dependent Hartree–Fock dynamics

We propose a framework to learn the time-dependent Hartree–Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Although the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange–correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to 60 × 60 × 60 × 60. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Anomalous Hall crystals in rhombohedral multilayer graphene. II. General mechanism and a minimal model

Here we propose a minimal "three-patch model"for the anomalous Hall crystal (AHC), a topological electronic state that spontaneously breaks both time-reversal symmetry and continuous translation symmetry. The proposal for this state is inspired by the recently observed integer and fractional quantum Hall states in rhombohedral multilayer graphene at zero magnetic field. There, interaction effects appear to amplify the effects of a weak moiré potential, leading to the formation of stable, isolated Chern bands. It has been further shown that Chern bands are stabilized in mean-field calculations even without a moiré potential, enabling a realization of the AHC state. Our model is built on the dissection of the Brillouin zone into patches centered around high-symmetry points. Within this model, the wave functions at high-symmetry points fully determine the topology and energetics of the state. We extract two quantum geometrical phases of the noninteracting wave functions that control the stability of the topologically nontrivial AHC state. The model predicts that the AHC state wins over the topological trivial Wigner crystal in a wide range of parameters, and agrees very well with the results of full self-consistent Hartree-Fock calculations of the rhombohedral multilayer graphene Hamiltonian.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Particle-hole asymmetric phases in doped twisted bilayer graphene

Twisted bilayer graphene (TBG) has emerged as a paradigmatic platform for exploring the interplay between strong interactions in a multi-band system with nearly flat bands, while offering unprecedented control over the filling fraction of electron/hole carriers. Despite much theoretical work, developing a comprehensive ab initio model for this system has proven challenging due to the inherent trade-off between accurately describing the band structure and incorporating the interactions within the Hamiltonian. Here, we constructed an extended multi-orbital Hubbard model, and performed Hartree-Fock (HF) calculations to explore its phase diagram across commensurate fillings. We found several nearly-degenerate insulating states at charge neutrality, all of which exhibit orbital orders. We also observed that most of the Hartree–Fock ground states exhibit a generalized valley Hund’s-like rule, resulting in valley polarization. Importantly, we show that the incorporation of the intra-valley and inter-valley exchange interactions is crucial to properly stabilize the ordered symmetry-broken states. In agreement with experiments, we find significant particle-hole asymmetry, which underscores the importance of using particle-hole asymmetric models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene. I. Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field

Recent experiments on rhombohedral pentalayer graphene with a substrate-induced moiré potential have identified both Chern insulators and fractional quantum Hall states at zero magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moiré lattice are weak, and seem to be readily accessed without fine-tuning. To address these experimental puzzles, we study a model of interacting electrons in this geometry. Within self-consistent Hartree-Fock (SCHF) calculations, we find an isolated Chern band with small bandwidth and good quantum geometry. Exact diagonalization and density-matrix renormalization group calculations both confirm the band hosts fractional quantum Hall states without a magnetic field. Remarkably, the Chern band is stable at a wide range of angles, at four through six rhombohedral layers, at varying rhombohedral hopping parameters, and—most strikingly—survives in SCHF calculations when the moiré potential vanishes. In this limit, the state spontaneously breaks time-reversal and translation symmetry simultaneously, giving a topological crystalline state that we term the “anomalous Hall crystal.” We argue this is a general mechanism to create stable Chern bands in rhombohedral multilayer graphene, opening the door to studying the interplay between electronic topology, fractionalization, and spontaneous translation symmetry breaking.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Pauli energy contribution to nucleus-nucleus interaction

The investigation delves into understanding how the Pauli exclusion principle influences the bare potential between atomic nuclei through the application of advanced theoretical methodologies. Specifically, the application of the novel Frozen-Hartree-Fock (DCFHF) technique is employed. The resulting potentials demonstrate a noticeable repulsion at short distances, attributed to the effects of the Pauli exclusion principle. To account for dynamic phenomena, such as nucleon transfer processes, the density-constrained time-dependent Hartree-Fock (DC-TDHF) method is utilized. This approach integrates isovector contributions into the potential, shedding light on their influence on fusion reactions. Notably, the inclusion of isovector effects leads to a reduction or enhancement in the inner part of the potential, suggesting a nuanced role of transfer in the fusion process.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Fragment-based initialization for quantum subspace methods

Here, we present a novel quantum-classical algorithm called LAS-QKSD for multireference systems, by combining a classical localized active space (LAS) fragment-based multireference algorithm with the quantum Krylov subspace diagonalization (QKSD) method for quantum computers. The algorithm uses wave function information from a LAS self-consistent field (LASSCF) calculation to prepare an initial state with better overlap with the target ground state than the Hartree-Fock state. This is coupled with the use of QKSD to ultimately converge to the exact energy, providing faster convergence than starting from the Hartree-Fock state. Fragmentation has the two-fold benefit of fewer configurations on the classical side of the algorithm as well as fewer state preparation gates on the quantum side. First, we compare the LAS-QKSD method to the classical LASSCF method and to QKSD with a Hartree-Fock initial state. We then examine ways to load the LASSCF wave function using direct initialization and a QKSD-motivated spectral filtering approach. Finally, using a bimetallic complex, we show that the LAS-QKSD method is an efficient alternative to highly expensive complete active space SCF (CASSCF) calculations on strongly correlated systems.

D'Cunha, Ruhee↗
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

Isospin composition of fission barriers

We employ a microscopic method to study how isospin affects the fission potential of 240 Pu. Our approach uses constrained Hartree-Fock theory (CHF) which allows us to separately investigate the isoscalar and isovector properties of the nuclear energy density functional (EDF). By analyzing the isoscalar and isovector components of the EDF along the fission path we can assess the isovector contribution to fission barriers. Here, we study this effect for the fully adiabatic path to scission. The isovector component of the fission potential is found to increase in magnitude as the nucleus evolves towards scission, exemplifying the importance of stringent constraints on the isovector sector of the nuclear EDF for reliable predictions of fission properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Efficient Monte Carlo event generation for neutrino-nucleus exclusive cross sections

Modern neutrino-nucleus cross section computations need to incorporate sophisticated nuclear models to achieve greater predictive precision. However, the computational complexity of these advanced models often limits their practicality for experimental analyses. To address this challenge, we introduce a new Monte Carlo method utilizing normalizing flows to generate surrogate cross sections that closely approximate those of the original model while significantly reducing computational overhead. As a case study, we built a Monte Carlo event generator for the neutrino-nucleus cross section model developed by the Ghent group. This model employs a Hartree-Fock procedure to establish a quantum mechanical framework in which both the bound and scattering nucleon states are solutions to the mean-field nuclear potential. The surrogate cross sections generated by our method demonstrate excellent accuracy with a relative effective sample size of more than 98.4%, providing a computationally efficient alternative to traditional Monte Carlo sampling methods for differential cross sections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Quantum state preparation with resolution refinement

We introduce a method called resolution refinement that allows one to bootstrap eigenstate preparation on a quantum computer. We first prepare an eigenstate of a low-resolution Hamiltonian using any method of choice. The eigenstate is then lifted to higher resolution and adiabatically evolved to produce the corresponding eigenstate of a higher-fidelity Hamiltonian. We give examples of resolution refinement applied to both single-particle basis states as well as a spatial lattice grid. For basis refinement, we compute few-body ground states of the Busch model for interacting particles in a harmonic trap in one dimension. For lattice refinement, we compute Hartree-Fock nuclear states for a central Woods-Saxon potential in three dimensions, and we compute bound states and continuum states in a multi-species Hubbard model of fermions in one dimension. In all cases, the method is efficient and requires an adiabatic evolution time that scales with the inverse of the energy gap times the square root of the system size. We show that this very favorable scaling arises from the fact that resolution refinement does not make large changes to the structure or energies of the low-energy eigenstates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Breaking the Million-Electron and 1 EFLOP/s Barriers: Biomolecular-Scale Ab Initio Molecular Dynamics Using MP2 Potentials

The accurate simulation of complex biochemical phenomena has historically been hampered by the computational requirements of high-fidelity molecular-modeling techniques. Quantum mechanical methods, such as ab initio wave-function (WF) theory, deliver the desired accuracy, but have impractical scaling for modeling biosystems with thousands of atoms. Combining molecular fragmentation with MP2 perturbation theory, this study presents an innovative approach that enables biomolecular-scale ab initio molecular dynamics (AIMD) simulations at WF theory level. Leveraging the resolution-of-the-identity approximation for Hartree-Fock and MP2 gradients, our approach eliminates computationally intensive four-center integrals and their gradients, while achieving near-peak performance on modern GPU architectures. The introduction of asynchronous time steps minimizes time step latency, overlapping computational phases and effectively mitigating load imbalances. Utilizing up to 9,400 nodes of Frontier and achieving 59% (1006.7 PFLOP/s) of its double-precision floating-point peak, our method enables us to break the million-electron and 1EFLOP/s barriers for AIMD simulations with quantum accuracy.

Kurzak, Jakub↗
DOE OSTI2024

A static quantum embedding scheme based on coupled cluster theory

Here, we develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment problem using a high-level CC method and address the environment problem with a lower-level Møller–Plesset (MP) perturbative method. This embedding approach inherits many conceptual developments from the hybrid second-order Møller–Plesset (MP2) and CC works by Nooijen [J. Chem. Phys. 111, 10815 (1999)] and Bochevarov and Sherrill [J. Chem. Phys. 122, 234110 (2005)]. We go beyond those works here by primarily targeting a specific localized fragment of a molecule and also introducing an alternative mechanism to relax the environment within this framework. We will call this approach MP-CC. We demonstrate the effectiveness of MP-CC on several potential energy curves and a set of thermochemical reaction energies, using CC with singles and doubles as the fragment solver, and MP2-like treatments of the environment. The results are substantially improved by the inclusion of orbital relaxation in the environment. Using localized bonds as the active fragment, we also report results for N=N bond breaking in azomethane and for the central C–C bond torsion in butadiene. We find that when the fragment Hilbert space size remains fixed (e.g., when determined by an intrinsic atomic orbital approach), the method achieves comparable accuracy with both a small and a large basis set. Additionally, our results indicate that increasing the fragment Hilbert space size systematically enhances the accuracy of observables, approaching the precision of the full CC solver.

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

Nonlinear Optimal Control of Electron Dynamics Within Hartree-Fock Theory

Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of motion—the time-dependent Schrödinger equation (TDSE)—is numerically intractable. Here, we present a solution of this problem within time-dependent Hartree-Fock (TDHF) theory, a mean field approximation of the TDSE. Optimality is defined in terms of minimizing the total control effort while maximizing the overlap between desired and achieved target states. We frame this problem as an optimization problem constrained by the nonlinear TDHF equations; we solve it using trust region optimization with gradients computed via a custom-built adjoint state method. For three molecular systems, we show that with very small neural network parametrizations of the control, our method yields solutions that achieve desired targets within acceptable constraints and tolerances.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

The approximate second order coupled-cluster method based on a size-consistent Brillouin–Wigner partitioning

We present a variant of the approximate second order coupled-cluster method (CC2) with a two-parameter size-consistent Brillouin–Wigner (BW-s) partitioning instead of a Møller–Plesset (MP) partitioning for the unperturbed Hamiltonian, which we refer to as BWs-CC2. The computational complexity of this model scales identically to CC2 with molecular size. Conventional CC2 and its regularized BWs-CC2 variants, as well as conventional MP2 and two of its regularized BW-s2 variants, were assessed on a 535 element database spanning thermochemistry, non-covalent interactions, barrier heights, and isomerization energies. To ensure a well-defined model chemistry, the assessment was performed using internally stable spin-polarized Hartree–Fock (HF) orbitals in the finite aug-cc-pVQZ basis without counterpoise corrections. As a result of using stable orbitals, contrary to conventional wisdom, we find that CC2 substantially outperforms MP2 on molecules with significantly spin contaminated reference orbitals without a significant increase in error on systems with a spin-pure reference, showing the value of its single substitutions. While no single choice of regularization parameters can be optimal for all datasets, we find that BWs-CC2 generally outperforms both CC2 and BW-s2 with a single judicious parameter choice. Additional tests on dipole moments and bond lengths of diatomics provide further support for the utility of this choice. Furthermore, the main outliers and poorest performing cases are associated with large amounts of spin-contamination in the HF reference, which is indicative of systems with either strong correlation or extensive artificial symmetry breaking. Overall, these findings argue that the perception of the quality of the CC2 ground state should be reevaluated and that it can be further improved upon by the soundly based BWs-CC2 variant with the recommended parameter choice.

Correlation energy↗
DOE OSTI2024

Simplified projection on total spin zero for state preparation on quantum computers

Here, we introduce a simple algorithm for projecting on J = 0 states of a many-body system by performing a series of rotations to remove states with angular momentum projections greater than zero. Existing methods rely on unitary evolution with the two-body operator J 2 , which when expressed in the computational basis contains many complicated Pauli strings requiring Trotterization and leading to very deep quantum circuits. Our approach performs the necessary projections using the one-body operators J x and J z . By leveraging the method of Cartan decomposition, the unitary transformations that perform the projection can be parametrized as a product of a small number of two-qubit rotations, with angles determined by an efficient classical optimization. Given the reduced complexity in terms of gates, this approach can be used to prepare approximate ground states of even-even nuclei by projecting onto the J = 0 component of deformed Hartree-Fock states. We estimate the resource requirements in terms of the universal gate set {H,S, CNOT ,T} and briefly discuss a variant of the algorithm that projects onto J = 1/2 states of a system with an odd number of fermions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Zero and Finite Temperature Quantum Simulations Powered by Quantum Magic

We introduce a quantum information theory-inspired method to improve the characterization of many-body Hamiltonians on near-term quantum devices. We design a new class of similarity transformations that, when applied as a preprocessing step, can substantially simplify a Hamiltonian for subsequent analysis on quantum hardware. By design, these transformations can be identified and applied efficiently using purely classical resources. In practice, these transformations allow us to shorten requisite physical circuit-depths, overcoming constraints imposed by imperfect near-term hardware. Importantly, the quality of our transformations is t u n a b l e : we define a 'ladder' of transformations that yields increasingly simple Hamiltonians at the cost of more classical computation. Using quantum chemistry as a benchmark application, we demonstrate that our protocol leads to significant performance improvements for zero and finite temperature free energy calculations on both digital and analog quantum hardware. Specifically, our energy estimates not only outperform traditional Hartree-Fock solutions, but this performance gap also consistently widens as we tune up the quality of our transformations. In short, our quantum information-based approach opens promising new pathways to realizing useful and feasible quantum chemistry algorithms on near-term hardware.

Physics↗
DOE OSTI2025

Role of effective mass and long-range interactions in the band-gap renormalization of photoexcited semiconductors

Understanding how to control changes in the electronic structure and related dynamical renormalizations by external driving fields is the key for understanding ultrafast spectroscopy and applications in electronics. Here, we focus on the band gap's modulation by external electric fields and uncover the effect of band dispersion on the gap renormalization. We employ the Green's function formalism using the real-time Dyson expansion to account for dynamical correlations induced by photodoping. The many-body formalism captures the dynamics of systems with long-range interactions, carrier mobility, and variable electron and hole effective mass. We also demonstrate that mean-field simulations based on the Hartree-Fock Hamiltonian, which lacks dynamical correlations, yields a qualitatively incorrect picture of band-gap renormalization. We find the trend that increasing effective mass, thus decreasing mobility, leads to as much as a 6% enhancement in band-gap renormalization. Further, the renormalization is strongly dependent on the degree of photodoping. As the screening induced by free electrons and holes effectively reduces any long-range and interband interactions for highly excited systems, we show that there is a specific turnover point with a minimal band gap. Here, we further demonstrate that the optical gap renormalization follows the same trend though its magnitude is altered by the Moss-Burstein effect.

Approximation methods for many-body systems↗