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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions

Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.

Dyall, Kenneth G.↗
DOE OSTI2020

Finite-temperature many-body perturbation theory in the grand canonical ensemble

A finite-temperature many-body perturbation theory is presented, which expands in power series the electronic grand potential, chemical potential, internal energy, and entropy on an equal footing. Sum-over-states and sum-over-orbitals analytical formulas for the second-order perturbation corrections to these thermodynamic properties are obtained in a time-independent, nondiagrammatic, algebraic derivation, relying on the sum rules of the Hirschfelder–Certain degenerate perturbation energies in a degenerate subspace as well as nine algebraic identities for the zeroth-order thermal averages of one- through four-indexed quantities and products thereof. Lastly, they reproduce numerically exactly the benchmark data obtained as the numerical derivatives of the thermal-full-configuration-interaction results for a wide range of temperatures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Diagonalizing the Born–Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom

This article describes a method for calculating higher order or nonadiabatic corrections in Born–Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner–Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ 2 , where κ = (m/M)1/4 is the usual Born–Oppenheimer parameter. The lowest order term is the usual Born–Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born–Oppenheimer theory. Here, we show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born–Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2020

Application of dilaton chiral perturbation theory to N f = 8 , SU(3) spectral data

We extend dilaton chiral perturbation theory (dChPT) to include the taste splittings in the Nambu-Goldstone sector observed in lattice simulations of near-conformal theories with staggered fermions. We then apply dChPT to a recent simulation by the LSD collaboration of the SU(3) gauge theory with 8 fermions in the fundamental representation, which is believed to exhibit near-conformal behavior in the infrared, and in which a light singlet scalar state, nearly degenerate with the pions, has been found. We find that the mesonic sector of this theory can be successfully described by dChPT, including, in particular, the mesonic taste splittings found in the simulation. We confirm that current simulations of this theory are in the "large-mass" regime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Cluster perturbation theory X: A parallel implementation of Lagrangian perturbation series for the coupled cluster singles and doubles ground-state energy through fifth order

We describe an efficient implementation of cluster perturbation and Møller-Plesset Lagrangian energy series through fifth order that target the coupled cluster singles and doubles energy utilizing the resolution of the identity approximation. We illustrate the computational performance of the implementation by performing ground state energy calculations on systems with up to 1200 basis functions using a single node and by comparison to conventional CCSD calculations. We further show that our hybrid MPI/OMP parallel implementation that also utilizes graphical processing units can be used to obtain fifth order energies on systems with almost 1200 basis functions with a 90 minute "time to solution" running on Frontier at Oak Ridge National Laboratory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1977

Diagrammatic perturbation theory applied to the ground state of the water molecule

The diagrammatic many-body perturbation theory is applied to the ground state of the water molecule within the algebraic approximation. Using four different basis sets, the total energy, the equilibrium OH bond length, and the equilibrium HOH bond angle are examined. The latter is found to be a particularly sensitive test of the convergence of perturbation expansions. Certain third-order results, which incorporate all two-, three-, and four-body effects, show evidence of good convergence properties.

Silver, D. M.↗
DOE OSTI2023

Amplitude/operator basis in chiral perturbation theory

We establish a systematic construction of the on-shell amplitude/operator basis for Chiral Perturbation Theory (ChPT) in D = 4 spacetime dimensions and with an arbitrary number of flavors N f . For kinematic factors, we employ spinor-helicity variables to construct the soft blocks, which are local amplitudes satisfying the Adler’s zero condition, as well as to take into account the reduction in the kinematic basis due to the Gram determinant, which arises at O(p 10 ) when the number of multiplicity N in an amplitude becomes large: N > D. For flavor factors, we include group-theoretic relations at small N f , N f ≤ N, which decreases the flavor basis. The result is obtained by adapting the Young tensor method of constructing the operator basis for generic effective field theories to the case of non-linearly realized symmetries. Working in the massless quark limit, we present purely mesonic operators for both even- and odd-parity at O(p 6 ) and O(p 8 ) for N = 6 and arbitrary N f , and establish a direct correspondence between the amplitude basis and the operator basis. Furthermore, the redundancy due to the Gram determinant is studied at O(p 10 ) for N = 6, 8 and 10.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Ab initio electron-two-phonon scattering in GaAs from next-to-leading order perturbation theory

Electron-phonon (e–ph) interactions are usually treated in the lowest order of perturbation theory. Here we derive next-to-leading order e–ph interactions, and compute from first principles the associated electron-two-phonon (2ph) scattering rates. The derivations involve Matsubara sums of two-loop Feynman diagrams, and the numerical calculations are challenging as they involve Brillouin zone integrals over two crystal momenta and depend critically on the intermediate state lifetimes. Using Monte Carlo integration together with a self-consistent update of the intermediate state lifetimes, we compute and converge the 2ph scattering rates, and analyze their energy and temperature dependence. We apply our method to GaAs, a weakly polar semiconductor with dominant optical-mode long-range e–ph interactions. We find that the 2ph scattering rates are as large as nearly half the value of the one-phonon rates, and that including the 2ph processes is necessary to accurately predict the electron mobility in GaAs from first principles.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Pion-nucleon scattering in baryon chiral perturbation theory combined with the 1/𝑁 𝑐 expansion

This work implements the combined baryon chiral perturbation theory (BChPT) and 1/𝑁 𝑐 expansions for pion-nucleon elastic scattering. The effective theory is based on the baryon sector dynamical spin-flavor 𝑆⁢𝑈⁡(4) symmetry emergent in the large 𝑁 𝑐 limit, whose breaking is controlled by the 1/𝑁 𝑐 expansion. The noncommutativity of the chiral and 1/𝑁 𝑐 expansions in unitarity corrections (loops) requires a linking of both expansions. As it was shown in the case of baryon masses and currents, the natural linking is the 𝜉 expansion, in which 𝒪⁡(𝑝) = 𝒪⁡(1/𝑁 𝑐 ) = 𝒪⁡(𝜉). The spin-flavor symmetry requires that the ground state baryons span an 𝑆⁢𝑈⁡(4) symmetric irreducible representation which implies that in particular 𝑁 and Δ are active degrees of freedom in the effective theory. The scattering amplitude is expanded to the next-to-next-to leading order in the 𝜉 expansion, corresponding to the one-loop contributions with the leading-order Lagrangian. The results are given for generic 𝑁 𝑐 in order to demonstrate the consistency of the framework. The spin-flavor symmetry plays a central role in maintaining the consistency of the effective theory with respect to the 1/𝑁 𝑐 expansion. This consistency manifests itself in an improvement in the convergence of the low energy expansion with respect to the case of the ordinary BChPT without an explicit dynamical Δ, which is known to be inconsistent with the constraints of 𝑁 𝑐 scaling. Fits to the 𝜋⁢𝑁 → 𝜋⁢𝑁, 𝑆, 𝑃, and 𝐷 partial wave amplitudes from the SAID data base are finally used to test the framework and to determine the energy range of its applicability.

Jayakodige, D. [Hampton Univ., Hampton, VA (United↗
DOE OSTI2026

One-Step Relativistic Driven Similarity Renormalization Group Multireference Perturbation Theory

We present an efficient implementation of a one-step relativistic second-order multireference perturbation theory based on the multireference driven similarity renormalization group (MR-DSRG) using the exact two-component (X2C) Hamiltonian, which we denote X2C-DSRG-MRPT2. We show that the X2C-DSRG-MRPT2 method can accurately capture spin–orbit coupling (SOC) effects in the electronic structure of strongly correlated systems containing elements across the periodic table. We further demonstrate that the X2C-DSRG-MRPT2 method, through its variational treatment of SOC effects, can yield spin–orbit splittings with mean absolute percentage errors consistently below 7% with respect to experimental values for systems containing up to sixth row elements. With its modest computational scaling (fourth power in system size for the perturbative step) and high accuracy, X2C-DSRG-MRPT2 provides a promising avenue for the routine treatment of relativistic effects in strongly correlated molecular systems.

Hamiltonians↗
DOE OSTI2022

Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost

Hybrid or “extended” symmetry-adapted perturbation theory (XSAPT) replaces traditional SAPT’s treatment of dispersion with better performing alternatives while at the same time extending two-body (dimer) SAPT to a many-body treatment of polarization using a self-consistent charge embedding procedure. The present work presents a systematic study of how XSAPT interaction energies and energy components converge with respect to the choice of Gaussian basis set. Errors can be reduced in a systematic way using correlation-consistent basis sets, with aug-cc-pVTZ results converged within <0.1 kcal/mol. Similar (if slightly less systematic) behavior is obtained using Karlsruhe basis sets at much lower cost, and we introduce new versions with limited augmentation that are even more efficient. Pople-style basis sets, which are more efficient still, often afford good results if a large number of polarization functions are included. The dispersion models used in XSAPT afford much faster basis-set convergence as compared to the perturbative description of dispersion in conventional SAPT, meaning that “compromise” basis sets (such as jun-cc-pVDZ) are no longer required and benchmark-quality results can be obtained using triple-ζ basis sets. The use of diffuse functions proves to be essential, especially for the description of hydrogen bonds. As a result, the “δ(Hartree–Fock)” correction for high-order induction can be performed in double-ζ basis sets without significant loss of accuracy, leading to a mixed-basis approach that offers 4× speedup over the existing (cubic scaling) XSAPT approach.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1995

Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

Melott, A. L.↗
DOE OSTI2020

Modeling features in the redshift-space halo power spectrum with perturbation theory

In this work, we study the ability of perturbative models with effective field theory contributions and infra-red resummation to model the redshift space clustering of biased tracers in models where the linear power spectrum has "features"- either imprinted during inflation or induced by non-standard expansion histories. We show that both Eulerian and Lagrangian perturbation theory are capable of reproducing the Fourier space two-point functions of halos up to the non-linear scale from a suite of 40963 particle N-body simulations. This is the first demonstration that perturbative models can accurately fit the redshift-space clustering of biased tracers in N-body simulations of such theories. By comparing different theoretical models and IR resummation schemes we assess the current theoretical uncertainty in predicting power spectra for models with features. Our results suggest that future surveys will be able to detect or tightly constrain features in the primordial spectrum below the one percent level across a wide range of scales.

redshift surveys↗
DOE OSTI2024

Phonon Thermal Transport in UO 2 via Self-Consistent Perturbation Theory

Computing thermal transport from first-principles in UO 2 is complicated due to the challenges associated with Mott physics. Here, we use irreducible derivative approaches to compute the cubic and quartic phonon interactions in UO 2 from first principles, and we perform enhanced thermal transport computations by evaluating the phonon Green’s function via self-consistent diagrammatic perturbation theory. Our predicted phonon lifetimes at T = 600 K agree well with our inelastic neutron scattering measurements across the entire Brillouin zone, and our thermal conductivity predictions agree well with previous measurements. Finally, both the changes due to thermal expansion and self-consistent contributions are nontrivial at high temperatures, though the effects tend to cancel, and interband transitions yield a substantial contribution.

36 MATERIALS SCIENCE↗