SEARCH · Engineering Papers

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

All sources NASA NTRS DOE OSTI

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↗

NASA NTRS1993

Structure and thermochemistry of ClO2 radicals

The structure of ClO2 has been calculated for the X 2A-double prime ground state using unrestricted Hartree-Fock (UHF), unrestricted second-order Moller-Plesset perturbation (UMP2), configuration interaction employing single and double excitation (CISD), and quadratic configuration interaction (QCI) ab initio molecular orbital methods. Calculations using UMP2 and CISD wave functions predict a ClO bond length of 1.728 +/- 0.01 A. The single-configuration-based QCI in the singles and doubles space with perturbation inclusion of triple substitutions, denoted QCISD(T), yield a ClO bond length of 2.205 A. The QCI results are consistent with results of Jensen (1990) who showed that the ClO bond length is 2.181 A using annihilated self-consistent methods (AUMP2). The thermochemistry of ClO2 radical has been calculated using MP2 and QCI methods employing an isodesmic scheme. Our scheme predicts the heat of formation for ClO2 at 0 K to be 24.6 +/- 2 kcal/mol.

Francisco, J. S.↗

NASA NTRS1974

Multiconfiguration self-consistent-field calculation of the dipole moment function of CO/X 1 sigma +/

Using the optimized valence configurations (OVC) multiconfiguration self-consistent-field (MCSCF) method, the dipole moment function for the ground state of CO in the vicinity of the equilibrium internuclear distance has been calculated. The OVC MCSCF calculation results are compared with existing Hartree-Fock and configuration interaction treatments of this molecule at single points and also the dipole moment function deduced from experimental infrared intensities. A general prescription for constructing OVC wavefunctions for diatomic molecules is also presented.

Billingsley, F. P., II↗

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↗

NASA NTRS1971

Deformed Brueckner-Hartree-Fock calculation for light nuclei

For the first time the Brueckner-Hartree-Fock (BHF) method was applied to nuclei whose intrinsic structure is nonspherical. One aim was to investigate whether the energy dependent reaction matrix calculated from a realistic nucleon-nucleon interaction leads to deformations similar to, or different from, those obtained from energy independent interactions in Hartree-Fock (HF) calculations. Reaction matrix elements were calculated as a function of starting energy for the Hamada-Johnston interaction, using a Pauli operator appropriate to O-16 and a shifted oscillator spectrum for virtual excited states. Binding energies, single-particle energies, radii, and shape deformations of the intrinsic state in unrenormalized as well as renormalized BHF are discussed and compared with previous HF studies. Results are presented for C-12, O-16, and Ne-20.

Braley, R. C.↗

NASA NTRS1967

The use of projection in SCF spin density calculations.

Spin-projected unrestricted self-consistent field /SCF/ methods for spin density calculations used to determine hyperfine coupling constants

SPIN-ORBIT INTERACTION↗

NASA NTRS1974

Approximate spin projection of three-component UHF wavefunctions - The states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5/2-/

The approximate spin projection method of Amos et al. is extended to handle UHF wave functions having three significant components of differing multiplicity. An expression is given for the energy after single annihilation which differs from that of Amos and Hall. The new expression reproduces the results obtained from a previous exact calculation for which the weights and energies of the components are known. The extended approximate projection method is applied to the pi-electron UHF wave functions for the ground states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5(2-). The results indicate a triplet ground state for the former and a singlet ground state for the latter, in agreement with experimental ESR susceptibility measurements for these molecular ions. C5C15(-) cannont be treated by restricted Hartree-Fock theory, due to its open-shell ground state. Incorrect results are obtained for the croconate dianion, if restricted Hartree-Fock theory and singly excited configuration interactions are utilized.

Phillips, D. H.↗

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↗

NASA NTRS1979

Finite-field Calculations of Molecular Polarizabilities Using Field-Induced Polarization Functions: Second- and Third-order Perturbation Correlation Corrections to the Coupled Hartree-Fock Polarizability of H2O

Ordinary Rayleigh-Schroudinger perturbation theory with Moller-Plesset (RSMP) partitioning is used to calculate second- and third-order correlation corrections to the CHF polarizability and dipole moment of the water molecule by a finite-field procedure. Pade approximants are found to be useful in accelerating the convergence of the property perturbation expansions. Field-induced polarization functions suitable for polarizability calculations are determined. The average polarizability calculated, neglecting vibrational averaging, with Dunning's (9s5p/4s-4s2p/2s) contracted GTO basis set augmented by field-induced lslp2d/lp polarization functions is within 3 per cent of the experimental result. Correlation corrections to the dipole moment and polarizability of the water molecule calculated by the finite-field RSMP and single + double excitation CI(SDCI) methods for the same basis set are found to be in close agreement. The RSMP approach has the advantages of being size-consistent and of being capable of greater efficiency than the SCDI method. Comparative calculations carried out using Epstein-Nesbet partitioning show that through third order RSEN correlation perturbation expansions for the dipole moment and polarizability are less rapidly convergent than RSMP expansions. However, reasonable accord with RSMP results can be achieved by using Pade approximants to accelerate the convergence of RSEN energy perturbation expansions. The convergence of RSMP property correlation expansions based on the zeroth-order uncoupled-Hartree-Fock (UCHF) and coupled-Hartree-Fock (CHF) approximations are compared through third order. Whereas the CHF + RSMP expansions are for practical purposes fully converged, the UCHF + RSMP expansions are not adequately converged.

Langhoff, S. R.↗

NASA NTRS1972

Ionization of multielectron atoms by fast charged particles.

Using plane waves to describe the incident and scattered particles, and screened hydrogenic and Coulomb functions to describe the atomic electrons before and after ejections, we have calculated the differential and total ionization cross sections of 11 atoms and one ion by electron impact, and ionization of helium by proton impact. The effective charges of the screened hydrogenic functions are fixed by the Hartree-Fock calculations. Calculations have been carried out for the atomic s, p, and d electrons. For low atomic numbers, we find reasonable agreement with the experimental data. For intermediate atomic numbers, we expect our results to overestimate the actual cross sections, since our choice of a unit charge for the Coulomb function of the ejected electrons will overestimate the atomic dipole potential strength, and in turn the high-energy cross sections. The advantage of the method presented here is that the ionization amplitude is given in analytic form. This may allow further analysis on this amplitude, and facilitates extension of the numerical integration for the cross section to high impact energies.

Omidvar, K.↗

NASA NTRS1987

Near Hartree-Fock quality GTO basis sets for the second-row atoms

Energy optimized, near Hartree-Fock quality Gaussian basis sets ranging in size from (17s12p) to (20s15p) are presented for the ground states of the second-row atoms for Na(2P), Na(+), Na(-), Mg(3P), P(-), S(-), and Cl(-). In addition, optimized supplementary functions are given for the ground state basis sets to describe the negative ions, and the excited Na(2P) and Mg(3P) atomic states. The ratios of successive orbital exponents describing the inner part of the 1s and 2p orbitals are found to be nearly independent of both nuclear charge and basis set size. This provides a method of obtaining good starting estimates for other basis set optimizations.

Partridge, Harry↗

NASA NTRS1987

Near Hartree-Fock quality GTO basis sets for the second-row atoms

Partridge, Harry↗

DOE OSTI2024

Search for beyond-mean-field signatures in heavy-ion fusion reactions

Examination of high-resolution, experimental fusion excitation functions for 16,17,18 O + 12 C reveals a remarkable irregular behavior that is rooted in the structure of both the colliding nuclei and the quasi-molecular composite system. The impact of the l-dependent fusion barriers is assessed using a time-dependent Hartree-Fock model, viewed as a mean-field reference. Barrier penetrabilities, taken directly from a density-constrained calculation, provide a significantly improved description of the experimental data as compared to the standard Hill-Wheeler approach. Furthermore, the remaining deviations between the parameter-free theoretical mean-field predictions and experimental fusion cross sections are exposed and discussed.

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↗