Search NASA⌕ Search

SEARCH · Search NASA

Results for “random phase approximation”

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.

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

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Introducing the embedded random phase approximation: H 2 dissociative adsorption on Cu(111) as an exemplar

The random phase approximation (RPA) as a means of treating electron correlation recently has been shown to outperform standard density functional theory (DFT) approximations in a variety of cases. However, the computational cost of the RPA is substantially more than DFT, especially when aiming to study extended surfaces. Properly accounting for sufficient surface ensemble size, Brillouin zone sampling, and vacuum separation of periodic images in standard periodic-planewave-based DFT code raises the cost to achieve converged results. Here, we show that sub-system embedding schemes enable use of the RPA for modeling heterogeneous reactions at reduced computational cost. Further, we explore two different embedded RPA (emb-RPA) approaches, periodic emb-RPA and cluster emb-RPA. We use the (experimentally and theoretically) well-studied H 2 dissociative adsorption on Cu(111) as our exemplar, and first perform full periodic RPA calculations as a benchmark. The full RPA results match well the semi-empirical barrier fit to experimental observables and others derived from high-level computations, e.g., from recent embedded n-electron valence second order perturbation theory [Zhao et al., J. Chem. Theory Comput. 16(11), 7078–7088 (2020)] and quantum Monte Carlo [Doblhoff-Dier et al., J. Chem. Theory Comput. 13(7), 3208–3219 (2017)] simulations. Among the two emb-RPA approaches tested, the cluster emb-RPA accurately reproduces the energy profile (maximum error of 50 meV along the reaction pathway) while reducing the computational cost by approximately two orders of magnitude. We therefore expect that the embedded cluster approach will enable wider RPA implementation in heterogeneous catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Exploring the Random Phase Approximation for Materials and Chemical Physics

In this work we test the performance of the fully nonlocal random phase approximation (RPA) for challenging problems in materials chemistry and physics. In this work we assessed the fully nonlocal random phase approximation (RPA) for the delicate energy differences of interest in materials chemistry and physics. The applications in this proposal are challenges for the simpler approximations of Kohn-Sham density functional theory, which are part of the current “standard model” for quantum chemistry and condensed matter physics. Direct RPA includes the full exact exchange energy and a nonlocal correlation energy from the occupied and unoccupied Kohn-Sham orbitals and orbital energies, with an approximate but universal description of long-range van der Waals attraction. RPA still cannot be a benchmark electronic structure method without a correction for its short-range correlation energy which is too deep. The short-range error of RPA can be corrected by a spatially nonlocal, exchange-only kernel. Such kernels could be a more reliable and “intrinsic” approximation to capture accurate ground-state energy differences than the expensive SOSEX and other beyond-RPA corrections. In this project we revealed the strengths and limitations of some model kernels through some materials problems focusing on structural phase transitions and transition metal chemistry. In addition we demonstrated the accuracy of the Renormalized RPA for total correlation energies of simple solids, and the pressure-induced phase transitions.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Embedded random phase approximation for magnetic systems: H 2 dissociative adsorption on Fe(110)

The random phase approximation (RPA), a method for treating electron correlation, has been shown to be superior to standard density functional theory (DFT) approximations in numerous cases. However, the RPA’s computational cost is substantially higher than that of DFT, particularly restricting its application to extended surfaces. The recently introduced embedded RPA (emb-RPA) approach [Wei et al., J. Chem. Phys. 159(19), 194108 (2023)] reduces this computational cost by approximately two orders of magnitude. While previous applications of emb-RPA focused on non-spin-polarized systems, here we extend the approach to ferromagnetic ones. Unlike other embedded correlated wavefunction methods, such as embedded complete active space self-consistent field theory, emb-RPA is advantageous for spin-polarized systems because the RPA is compatible with unrestricted DFT solutions, which are eigenfunctions of the spin angular momentum operator S z but not the total spin-squared operator S 2 . By applying emb-RPA with specific magnetization constraints, we achieved a speedup of two to three orders of magnitude (one order when accounting for the one-time embedding potential optimization cost) with only small errors (∼50 meV) compared to full periodic RPA. Moreover, emb-RPA significantly reduces the over-binding errors of DFT approximations. In conclusion, we anticipate that the acceleration enabled by the spin-polarized emb-RPA approach will broaden the applicability of RPA to magnetic materials.

Density functional theory↗
DOE OSTI2015

Linear-scaling implementation of the direct random-phase approximation

We report the linear-scaling implementation of the direct random-phase approximation (dRPA) for closed-shell molecular systems. As a bonus, linear-scaling algorithms are also presented for the second-order screened exchange extension of dRPA as well as for the second-order Møller–Plesset (MP2) method and its spin-scaled variants. Our approach is based on an incremental scheme which is an extension of our previous local correlation method [Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The approach extensively uses local natural orbitals to reduce the size of the molecular orbital basis of local correlation domains. In addition, we also demonstrate that using natural auxiliary functions [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], the size of the auxiliary basis of the domains and thus that of the three-center Coulomb integral lists can be reduced by an order of magnitude, which results in significant savings in computation time. The new approach is validated by extensive test calculations for energies and energy differences. Our benchmark calculations also demonstrate that the new method enables dRPA calculations for molecules with more than 1000 atoms and 10 000 basis functions on a single processor.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Calculating beta decay in the deformed self-consistent quasiparticle random phase approximation

We discuss a recent global calculation of beta-decay rates in the self-consistent Skyrme quasiparticle random phase approximation (QRPA), with axially symmetric nuclear deformation treated explicitly. The calculation makes makes use of the finite-amplitude method, first proposed by Nakatsukasa and collaborators, to reduce computation time. The results are comparable in quality to those of several other global QRPA calculations. The QRPA may have reached the limit of its accuracy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations

In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N{sup 4}). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S{sup ^2}〉 are also developed and tested.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Chiral NNLO sat descriptions of nuclear multipole resonances within the random-phase approximation

We study nuclear multipole resonances in the framework of the random-phase approximation by using the chiral potential NNLO sat . This potential includes two- and three-body terms that have been simultaneously optimized to low-energy nucleon-nucleon scattering data and selected nuclear structure data. Our main focuses have been the isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell nuclei, 4 He, 16,22,24 O, and 40,48 Ca. These resonance modes have been widely observed in experiment. In addition, we use a renormalized chiral potential Vlow-k, based on the N 3 LO two-body potential by Entem and Machleidt [Phys. Rev. C 68, 041001 (2011)]. This introduces a dependency on the cutoff parameter used in the normalization procedure as reported in previous works by other groups. While NNLO sat can reasonably reproduce observed multipole resonances, it is not possible to find a single cutoff parameter for the V low-k potential that simultaneously describes the different types of resonance modes. The sensitivity to the cutoff parameter can be explained by missing induced three-body forces in the calculations. Our results for neutron-rich 22,24 O show a mixing nature of isoscalar and isovector resonances in the dipole channel at low energies. We predict that 22 O and 24 O have low-energy isoscalar quadrupole resonances at energies lower than 5 MeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Gamow-Teller Strength in Ca 48 and Ni 78 with the Charge-Exchange Subtracted Second Random-Phase Approximation

Here, we develop a fully self-consistent subtracted second random-phase approximation for charge-exchange processes with Skyrme energy-density functionals. As a first application, we study Gamow-Teller excitations in the doubly magic nucleus 48 Ca, the lightest double-β emitter that could be used in an experiment, and in 78 Ni, the single-beta-decay rate of which is known. The amount of Gamow-Teller strength below 20 or 30 MeV is considerably smaller than in other energy-density-functional calculations and agrees better with experiment in 48 Ca, as does the beta-decay rate in 78 Ni. These important results, obtained without ad hoc quenching factors, are due to the presence of two-particle–two-hole configurations. Their density progressively increases with excitation energy, leading to a long high-energy tail in the spectrum, a fact that may have implications for the computation of nuclear matrix elements for neutrinoless double-β decay in the same framework.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Communication: Two-component ring-coupled-cluster computation of the correlation energy in the random-phase approximation

Within the framework of density-functional theory, the correlation energy is computed in the random-phase approximation (RPA) using spinors obtained from a two-component relativistic Kohn–Sham calculation accounting for spin–orbit interactions. Ring-coupled-cluster equations are solved to obtain the two-component RPA correlation energy. Results are presented for the hydrides of the halogens Br, I, and At as well as of the coinage metals Cu, Ag, and Au, based on two-component relativistic exact-decoupling Kohn–Sham calculations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Communication: An effective linear-scaling atomic-orbital reformulation of the random-phase approximation using a contracted double-Laplace transformation

An atomic-orbital (AO) reformulation of the random-phase approximation (RPA) correlation energy is presented allowing to reduce the steep computational scaling to linear, so that large systems can be studied on simple desktop computers with fully numerically controlled accuracy. Our AO-RPA formulation introduces a contracted double-Laplace transform and employs the overlap-metric resolution-of-the-identity. First timings of our pilot code illustrate the reduced scaling with systems comprising up to 1262 atoms and 10 090 basis functions. .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights

We consider several spin-unrestricted random-phase approximation (RPA) variants for calculating correlation energies, with and without range separation, and test them on datasets of atomization energies and reaction barrier heights. We show that range separation greatly improves the accuracy of all RPA variants for these properties. Moreover, we show that a RPA variant with exchange, hereafter referred to as RPAx-SO2, first proposed by Szabo and Ostlund [J. Chem. Phys. 67, 4351 (1977)] in a spin-restricted closed-shell formalism, and extended here to a spin-unrestricted formalism, provides on average the most accurate range-separated RPA variant for atomization energies and reaction barrier heights. Since this range-separated RPAx-SO2 method had already been shown to be among the most accurate range-separated RPA variants for weak intermolecular interactions [J. Toulouse et al., J. Chem. Phys. 135, 084119 (2011)], this works confirms range-separated RPAx-SO2 as a promising method for general chemical applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Optimization of Random Phase Approximation Calculations for Improved Energies of Molecules, Solids, and Surfaces

We present an optimized random phase approximation method (optRPA26) that significantly improves upon conventional RPA through an optimized choice of reference orbitals and energy components, rather than a modification of the RPA correlation functional itself. The method employs an empirically constructed hybrid functional to generate DFT orbitals to evaluate the RPA correlation energy, which is then scaled by a constant. Comprehensive benchmarks across molecules, bulk solids, and surface systems demonstrate that optRPA26 consistently achieves high accuracy, with mean absolute errors of 0.05 eV for W4-11-RE reaction energies, 0.07 eV for cohesive energies, 0.09 eV for metal oxide formation energies, 0.11–0.12 eV for adsorption of small molecules on metals, and 0.06 eV for adsorption on oxides. In addition, optRPA26 correctly captures phase stability in metal oxides and magnetic metals. The optRPA26 approach can be run using standard RPA implementations, highlighting its potential as a general-purpose reference method that can accurately capture covalent, ionic, metallic, and van der Waals bonding in molecules, solids, and interfaces.

Adsorption↗
DOE OSTI2016

Accurate and efficient calculation of excitation energies with the active-space particle-particle random phase approximation

An efficient method for calculating excitation energies based on the particle-particle random phase approximation (ppRPA) is presented. Neglecting the contributions from the high-lying virtual states and the low-lying core states leads to the significantly smaller active-space ppRPA matrix while keeping the error to within 0.05 eV from the corresponding full ppRPA excitation energies. The resulting computational cost is significantly reduced and becomes less than the construction of the non-local Fock exchange potential matrix in the self-consistent-field (SCF) procedure. With only a modest number of active orbitals, the original ppRPA singlet-triplet (ST) gaps as well as the low-lying single and double excitation energies can be accurately reproduced at much reduced computational costs, up to 100 times faster than the iterative Davidson diagonalization of the original full ppRPA matrix. For high-lying Rydberg excitations where the Davidson algorithm fails, the computational savings of active-space ppRPA with respect to the direct diagonalization is even more dramatic. The virtues of the underlying full ppRPA combined with the significantly lower computational cost of the active-space approach will significantly expand the applicability of the ppRPA method to calculate excitation energies at a cost of O(K^{4}), with a prefactor much smaller than a single SCF Hartree-Fock (HF)/hybrid functional calculation, thus opening up new possibilities for the quantum mechanical study of excited state electronic structure of large systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

Communication: Random phase approximation renormalized many-body perturbation theory

We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Random phase approximation with second-order screened exchange for current-carrying atomic states

The direct random phase approximation (RPA) and RPA with second-order screened exchange (SOSEX) have been implemented with complex orbitals as a basis for treating open-shell atoms. Both RPA and RPA+SOSEX are natural implicit current density functionals because the paramagnetic current density implicitly is included through the use of complex orbitals. We confirm that inclusion of the SOSEX correction improves the total energy accuracy substantially compared to RPA, especially for smaller-Z atoms. Computational complexity makes post self-consistent-field (post-SCF) evaluation of RPA-type expressions commonplace, so orbital basis origins and properties become important. Sizable differences are found in correlation energies, total atomic energies, and ionization energies for RPA-type functionals evaluated in the post-SCF fashion with orbital sets obtained from different schemes. Reference orbitals from Kohn-Sham calculations with semi-local functionals are more suitable for RPA+SOSEX to generate accurate total energies, but reference orbitals from exact exchange (non-local) yield essentially energetically degenerate open-shell atom ground states. RPA+SOSEX correlation combined with exact exchange calculated from a hybrid reference orbital set (half the exchange calculated from exact-exchange orbitals, the other half of the exchange from orbitals optimized for the Perdew-Burke-Ernzerhof (PBE) exchange functional) gives the best overall performance. Finally, numerical results show that the RPA-like functional with SOSEX correction can be used as a practical implicit current density functional when current effects should be included.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Charge transfer excitations from particle-particle random phase approximation—Opportunities and challenges arising from two-electron deficient systems

The particle-particle random phase approximation (pp-RPA) is a promising method for studying charge transfer (CT) excitations. Through a detailed analysis on two-electron deficient systems, we show that the pp-RPA is always able to recover the long-distance asymptotic –1/R trend for CT excitations as a result of the concerted effect between orbital energies and the pp-RPA kernel. We also provide quantitative results for systems with relatively short donor-acceptor distances. With conventional hybrid or range-separated functionals, the pp-RPA performs much better than time-dependent density functional theory (TDDFT), although it still gives underestimated results which are not as good as TDDFT with system-dependent tuned functionals. For pp-RPA, there remain three great challenges in dealing with CT excitations. First, the delocalized frontier orbitals in strongly correlated systems often lead to difficulty with self-consistent field convergence as well as an incorrect picture with about half an electron transferred. Second, the commonly used density functionals often underestimate the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (LUMO) for the two-electron deficient species, resulting in systems with delocalized orbitals. Third, the performance of pp-RPA greatly depends on the energy difference between the LUMO and a higher virtual orbital. However, the meaning of the orbital energies for higher virtual orbitals is still not clear. We also discuss the performance of an approximate pp-RPA scheme that uses density functional tight binding (pp-DFTB) as reference and demonstrate that the aforementioned challenges can be overcome by adopting suitable range-separated hybrid functionals. Here, the pp-RPA and pp-DFTB are thus promising general approaches for describing charge transfer excitations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Optimization of the Jastrow factor using the random-phase approximation and a similarity-transformed Hamiltonian: Application to band-structure calculation for some semiconductors and insulators

Based on the random-phase approximation and the transcorrelated (TC) method, we optimize the Jastrow factor together with one-electron orbitals in the Slater determinant in the correlated wave function with a new scheme for periodic systems. The TC method is one of the promising wave function theories for first-principles electronic structure calculation, where the many-body wave function is approximated as a product of a Slater determinant and a Jastrow factor, and the Hamiltonian is similarity-transformed by the Jastrow factor. Using this similarity-transformed Hamiltonian, we can optimize the one-electron orbitals without evaluating 3N-dimensional integrations for the N-electron system. In contrast, optimization of the Jastrow factor within the framework of the TC method is computationally much more expensive and has not been performed for solid-state calculations before. In this study, we also benefit from the similarity-transformation in optimizing the Jastrow factor. Our optimization scheme is tested in applications to some solids from narrow-gap semiconductors to wide-gap insulators, and it is verified that the band gap of a wide-gap insulator and the lattice constants of some solids are improved by this optimization with reasonable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Exploring the Random Phase Approximately for materials chemistry and physics

This proposal focuses on improved accuracy for the delicate energy differences of interest in materials chemistry with the fully nonlocal random phase approximation (RPA) in a density functional context. Could RPA or RPA-like approaches become standard methods of first-principles electronic-structure calculation for atoms, molecules, solids, surfaces, and nano-structures? Direct RPA includes the full exact exchange energy and a nonlocal correlation energy from the occupied and unoccupied Kohn-Sham orbitals and orbital energies, with an approximate but universal description of long-range van der Waals attraction. RPA also improves upon simple pair-wise interaction potentials or vdW density functional theory. This improvement is essential to capture accurate energy differences in metals and different phases of semiconductors. The applications in this proposal are challenges for the simpler approximations of Kohn-Sham density functional theory, which are part of the current “standard model” for quantum chemistry and condensed matter physics. Within this project we already applied RPA on different structural phase transitions on semiconductors, metals and molecules. Although RPA predicts accurate structural parameters, RPA has proven not equally accurate in all kinds of structural phase transitions. Therefore a correction to RPA can be necessary in many cases. We are currently implementing and testing a nonempirical, spatially nonlocal, frequency-dependent model for the exchange-correlation kernel in the adiabatic-connection fluctuation-dissipation context. This kernel predicts a nearly-exact correlation energy for the electron gas of uniform density. If RPA or RPA-like approaches prove to be reliably accurate, then expected increases in computer power may make them standard in the electronic-structure calculations of the future.

74 ATOMIC AND MOLECULAR PHYSICS↗