Theoretical study of atomic and molecular gases and their reactions in the upper atmosphere Summary report, 1 May - 31 Oct. 1965
Wave functions and total energy of energy states of diatomic molecules - Hartree-Fock calculation
Diatomic molecule↗
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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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Ab initio multireference study of the BN molecule
The lowest 1Sigma(+) and 3Pi states of the BN molecule are studied using multireference configuration interaction (MRCI) and averaged coupled-pair functional (ACPF) methods and large atomic natural orbital (ANO) basis sets, as well as several coupled cluster methods. Our calculations strongly support a 3Pi ground state, but the a1Sigma(+) state lies only 381 +/- 100/cm higher. The a1Sigma(+) state wave function exhibits strong multireference character and, consequently, the predictions of the perturbationally-based single-reference CCSD(T) coupled cluster method are not as reliable in this case as the multireference results. The theoretical predictions for the spectroscopic constants of BN are in good agreement with experiment for the Chi3Pi state, but strongly suggest a misassignment of the fundamental vibrational frequency for the a1Sigma(+) state.
Martin, J. M. L.↗
Unraveling the magnetic ground state in the alkali-metal lanthanide oxide Na 2 PrO 3
Here, a comprehensive set of muon spin spectroscopy and neutron scattering measurements supported by ab initio and model Hamiltonian simulations have been used to investigate the magnetic ground state of Na 2 PrO 3 . μSR reveals a Néel antiferromagnetic order below T N ~ 4.9K, with a small static magnetic moment m static ≤ 0.22 μ B /Pr collinearly aligned along the c axis. Inelastic neutron measurements reveal the full spectrum of crystal field excitations and confirm that the Pr 4+ ground-state wave function deviates significantly from the Γ 7 limit that is relevant to the Kitaev model. Single- and two-magnon excitations are observed in the ordered state below T N =4.6K and are well described by nonlinear spin wave theory from the Néel state using a magnetic Hamiltonian with Heisenberg exchange J=1 meV and symmetric anisotropic exchange Γ/J=0.1, corresponding to an XY model. Intense two magnon excitations are accounted for by g-factor anisotropy g z /g ± = 1.29. A fluctuating moment δm 2 = 0.57 (22) μ$^2_B$/Pr extracted from the energy and momentum integrated inelastic neutron signal is reduced from expectations for a local J = 1/2 moment with average g factor g avg ≈ 1.1. Together, the results demonstrate that the small moment in Na 2 PrO 3 arises from crystal field and covalency effects and the material does not exhibit significant quantum fluctuations.
36 MATERIALS SCIENCE↗
Effective field theory analysis of the Coulomb breakup of the one-neutron halo nucleus $$^{19}$$C
Abstract We analyse the Coulomb breakup of $$^{19}$$ 19 C measured at 67 A MeV at RIKEN. We use the Coulomb-Corrected Eikonal (CCE) approximation to model the reaction and describe the one-neutron halo nucleus $$^{19}$$ 19 C within Halo Effective Field Theory (Halo EFT). At leading order we obtain a fair reproduction of the measured cross section as a function of energy and angle. The description is insensitive to the choice of optical potential, as long as it accurately represents the size of $${}^{18}$$ 18 C. It is also insensitive to the interior of the $${}^{19}$$ 19 C wave function. Comparison between theory and experiment thus enables us to infer asymptotic properties of the ground state of $$^{19}$$ 19 C: these data put constraints on the one-neutron separation energy of this nucleus and, for a given binding energy, can be used to extract an asymptotic normalisation coefficient (ANC). These results are confirmed by CCE calculations employing next-to-leading order Halo EFT descriptions of $${}^{19}$$ 19 C: at this order the results for the Coulomb breakup cross section are completely insensitive to the choice of the regulator. Accordingly, this reaction can be used to constrain the one-neutron separation energy and ANC of $${}^{19}$$ 19 C.
Physics↗
Anisotropic excitonic magnetism from discrete C 4 symmetry in CeRhIn 5
Anisotropy in strongly correlated materials is a central parameter in determining the electronic ground state and is tuned through the local crystalline electric field. This is notably the case in the CeCo x Rh 1 − x In 5 system where the ground-state wave function can provide the basis for antiferromagnetism and/or unconventional superconductivity. We develop a methodology to understand the local magnetic anisotropy and experimentally investigate with neutron spectroscopy applied to antiferromagnetic ( T N = 3.8 K ) CeRhIn 5 , which is isostructural to d -wave superconducting ( T c = 2.3 K ) CeCoIn 5 . Through diagonalizing the local crystal field Hamiltonian with discrete tetragonal C 4 point group symmetry and coupling these states with the random phase approximation, we find two distinct modes polarized along the crystallographic c and a − b planes, agreeing with experiment. The anisotropy and bandwidth, underlying the energy scale of these modes, are tuneable with a magnetic field which we use experimentally to separate in energy single and multiparticle excitations thereby demonstrating the instability of excitations polarized within the crystallographic a − b plane in CeRhIn 5 . We compare this approach to a S eff = 1 2 parametrizations and argue for the need to extend conventional SU(2) theories of magnetic excitations to utilize the multilevel nature of the underlying crystal-field basis states constrained by the local point-group C 4 symmetry. Published by the American Physical Society 2024
Brener, D. J. (ORCID:0000000333400177)↗
Heuristic theory of positron-helium scattering.
An error in a previous modified adiabatic approximation (Drachman, 1966), due to a lack of generality in the form of the short-range correlation part of the wave function for L greater than zero, is corrected heuristically by allowing the monopole suppression parameter to depend on L. An L-dependent local potential is constructed to fit the well-known positron-hydrogen s, p, and d wave phase shifts below the rearrangement threshold. The same form of potential yields a positron-helium cross-section in agreement with a recent experimental measurement near threshold.
Drachman, R. J.↗
Hydrogen Bond Benchmark: Focal‐Point Analysis and Assessment of DFT Functionals
We performed a hierarchical, convergent ab initio benchmark study and systematically analyzed the performance of density functional approximations for describing hydrogen bonds in small neutral, cationic, and anionic complexes, as well as in larger systems involving amide, urea, deltamide, and squaramide moieties. Focal point analyses (FPA), extrapolating to the ab initio limit, were carried out using correlated wave function methods up to CCSDT(Q) for the small complexes and CCSD(T) for the larger systems, together with correlation-consistent Gaussian basis sets up to the complete basis set limit. Optimized geometries and vibrational frequencies were obtained at the CCSD(T) level. The resulting FPA hydrogen-bond energies converge within a few tenths of a kcal mol −1 . These reference data were used to evaluate 60 density functionals (including 12 dispersion-corrected), spanning the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. Overall, the meta-hybrid M06-2X provides the best performance for both hydrogen bond energies and geometries, while the dispersion-corrected GGAs BLYP-D3(BJ) and BLYP-D4 also yield accurate hydrogen-bond data and can serve as cost-effective options for studying large and complex systems.
coupled cluster theory↗
Multireference Methods are Realistic and Useful Tools for Modeling Catalysis
Abstract Highly correlated systems, in particular those that include transition metals, are ubiquitous in catalysis. The significant static correlation found in such systems is often poorly accounted for using Kohn Sham density functional theory methods, as they are single determinantal in nature. Applications to catalysis of more rigorous and appropriate multiconfigurational methods have been reported in select instances, but their use remains rare. We discuss obstacles that hinder the routine application of multireference (MR) wave function theoretical calculations to catalytic systems and the current state of the art with respect to removing those obstacles.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Weighted nodal domain averages of eigenstates for quantum Monte Carlo and beyond
In this report we study the nodal properties of many-body eigenstates of stationary Schrödinger equation that affect the accuracy of real-space quantum Monte Carlo calculations. In particular, we introduce weighted nodal domain averages that provide a new probe of nodal surfaces beyond the usual expectations. Particular choices for the weight function reveal, for example, that the difference between two arbitrary fermionic eigenvalues is given by the nodal hypersurface integrals normalized by overlaps with the bosonic ground state of the given Hamiltonian. Noninteracting and fully interacting Be atom with corresponding almost exact and approximate wave functions are used to illustrate several aspects of these concepts. Variational formulations that employ different weights are proposed for prospective improvement of nodes in variational and fixed-node diffusion Monte Carlo calculations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Shadow Lagrangian dynamics for superfluidity
Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is forced to follow the wave function of the quantum state through a rapidly oscillating extended harmonic oscillator. By considering the adiabatic limit for large frequencies of the harmonic oscillator, we can derive the two equations of motions, a Schrödinger-type equation for the quantum state and a wave equation for the extended field variable. The equations are coupled in a nonlinear way, but each equation individually is linear with respect to the variable that it defines. The computational advantage of this new system is that it can be easily discretized using linear time stepping methods, where we propose to use a Crank-Nicolson-type approach for the Schrödinger equation and an extended leapfrog scheme for the wave equation. Furthermore, the difference between the quantum state and the extended field variable defines a consistency error that should go to zero if the frequency tends to infinity. By coupling the time-step size in our discretization to the frequency of the harmonic oscillator we can extract an easily computable consistency error indicator that can be used to estimate the numerical error without additional costs. The findings are illustrated in numerical experiments.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Multi-Disciplinary Design Optimization Using WAVE
The current preliminary design tools lack the product performance, quality and cost prediction fidelity required to design Six Sigma products. They are also frequently incompatible with the tools used in detailed design, leading to a great deal of rework and lost or discarded data in the transition from preliminary to detailed design. Thus, enhanced preliminary design tools are needed in order to produce adequate financial returns to the business. To achieve this goal, GEAE has focused on building the preliminary design system around the same geometric 3D solid model that will be used in detailed design. With this approach, the preliminary designer will no longer convert a flowpath sketch into an engine cross section but rather, automatically create 3D solid geometry for structural integrity, life, weight, cost, complexity, producibility, and maintainability assessments. Likewise, both the preliminary design and the detailed design can benefit from the use of the same preliminary part sizing routines. The design analysis tools will also be integrated with the 3D solid model to eliminate manual transfer of data between programs. GEAE has aggressively pursued the computerized control of engineering knowledge for many years. Through its study and validation of 3D CAD programs and processes, GEAE concluded that total system control was not feasible at that time. Prior CAD tools focused exclusively on detail part geometry and Knowledge Based Engineering systems concentrated on rules input and data output. A system was needed to bridge the gap between the two to capture the total system. With the introduction of WAVE Engineering from UGS, the possibilities of an engineering system control device began to formulate. GEAE decided to investigate the new WAVE functionality to accomplish this task. NASA joined GEAE in funding this validation project through Task Order No. 1. With the validation project complete, the second phase under Task Order No. 2 was established to develop an associative control structure (framework) in the UG WAVE environment enabling multi-disciplinary design of turbine propulsion systems. The capabilities of WAVE were evaluated to assess its use as a rapid optimization and productivity tool. This project also identified future WAVE product enhancements that will make the tool still more beneficial for product development.
Irwin, Keith↗
The graviton four-point function in de Sitter space
We compute the tree-level late-time graviton four-point correlation function, and the related quartic wavefunction coefficient, for Einstein gravity in de Sitter spacetime. We derive this result in several ways: by direct calculation, using the in-in formalism and the wavefunction of the universe; by a heuristic derivation leveraging the flat space wave-function coefficient; and by using the boostless cosmological bootstrap, in particular the combination of the cosmological optical theorem, the amplitude limit, and the manifestly local test. We find agreement among the different methods.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
First principles study of the Fermi surface topology of CeCu 2 Si 2
Since the discovery of heavy-fermion superconductivity in CeCu 2 Si 2 , the material has attracted great interest, particularly with regard to the nature of the superconducting pairing and its mechanism. Consequently, it is essential to better understand the electronic Fermi surface topology and its role in strong antiferromagnetic fluctuations. The standard density functional theory method is insufficient to model the interplay of strong on-site Coulomb repulsion in localized 4𝑓 electrons and their hybridization with itinerant ligand-orbital electrons. We have performed electronic ground-state calculations on CeCu 2 Si 2 using the Gutzwiller wave function approximation. The Gutzwiller approximation captures the quasiparticle band renormalization from the strong on-site Coulomb repulsion. We have performed an analysis of this effect on the electronic structure and the Fermi surface topology by varying the interaction strength and taking into account the crystal-field splitting. Using the de Haas-van Alphen effect, the extremal Fermi surface cross-sectional areas were calculated to quantify the effects of quasiparticle mass renormalization on the Fermi surface. Our results confirm the presence of two Fermi surface sheets corresponding to the heavy (488𝑚 𝑒 ) and light (4.35𝑚 𝑒 ) quasiparticles when the crystal-field splitting is accounted for on equal footing with the electronic correlations. This method gives the best agreement with experimental measurements as well as the renormalized band method.
36 MATERIALS SCIENCE↗
A spectral domain method for remotely probing stratified media
The problem of remotely probing a stratified, lossless, dielectric medium is formulated using the spectral domain method of probing. The response of the medium to a spectrum of plane waves incident at various angles is used to invert the unknown profile. For TE polarization, the electric field satisfies a Helmholtz equation. The inverse problem is solved by means of a new representation for the wave function. The principal step in this inversion is solving a second kind Fredholm equation which is very amenable to numerical computations. Several examples are presented including some which indicate that the method can be used with experimentally obtained data. When the fields exhibit a surface wave behavior, a unique inversion can be obtained only if information about the magnetic field is also available. In this case, the inversion is accomplished by a two-step procedure which employs a formula of Jost and Kohn. Some examples are presented, and an approach which greatly shortens the computations without greatly deteriorating the results is discussed.
Schaubert, D. H.↗
Transverse structure of the pion beyond leading twist with basis light-front quantization
We investigate the twist-3transverse-momentum-dependent parton distribution functions (TMDs) of the pion with basis light-front quantization. The twist-3 TMDs are not independent and can be decomposed into twist-2and genuine twist-3 terms from the equations of motion (EOM). We compute the TMDs from the resulting light-front wave functions obtained by diagonalizing the light-front QCD Hamiltonian, determined for pion’s constituent quark-antiquark and quark-antiquark-gluon Fock sectors, with three-dimensional confinement. We also obtain the twist-3 parton distribution functions (PDFs) and show that they preserve the sum rule, which affirms the robustness of our approach. This is the first time that theoretical predictions are made for subleading twist structures of the pion containing interference terms between two light-front Fock sectors.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Nonadiabatic dynamics of photoexcited thiopyridone isomers: An interplay between El-Sayed’s conditions and energy gap law
We investigated the non-adiabatic dynamics of photoexcited thiopyridone systems across their ortho-, meta-, and para-isomeric forms. The relaxation pathways of the three isomers in both gas phase and solvent environments are mapped using surface hopping dynamics based on time-dependent density functional theory. Our analysis highlights the influence of isomeric structures on photophysical behavior, offering insights into design principles to control photochemical phenomena. The simulations suggest a systematic reduction in the rate of intersystem crossing (ISC) from ortho- to meta- to para-isomer. Comparisons with multiconfigurational wave function methods in the gas phase further demonstrate how electronic structure influences the predicted dynamical pathways. The simulated dynamics demonstrates that the spin–orbit coupling strength alone does not determine the rate of ISC, as both state energetics and underlying electronic and structural features play decisive roles. These aspects explain the much slower ISC in the para-isomer, as well as the non-negligible role of the El-Sayed forbidden pathway in the computed ISC dynamics.
Complete-active space self-consistent field↗
Diverse electronic topography in a distorted kagome metal LaTi 3 Bi 4
Recent reports on a family of kagome metals of the form 𝐿𝑛Ti 3 Bi 4 (𝐿𝑛 = Lanthanide) have stoked interest due to the combination of highly anisotropic magnetism and a rich electronic structure. The electronic structure near the Fermi level is proposed to exhibit Dirac points and van Hove singularities (VHSs). Here, in this manuscript, we use angle-resolved photoemission spectroscopy measurements in combination with density functional theory calculations to investigate the electronic structure of an interesting kagome metal LaTi 3 Bi 4 . Our results reveal multiple VHSs with one VHS located in the vicinity of the Fermi level. We clearly observe two flat bands, which originate from the destructive interference of wave functions within the Ti kagome motif. These flat bands and VHSs originate from Ti 𝑑 orbitals and are very responsive to the polarization of the incident beam. We notice a significant anisotropy in the electronic structure, resulting from the breaking of sixfold rotational symmetry in this material. Our findings demonstrate this member of Ti based kagome materials as a promising platform to explore novel emerging phenomena in the wider 𝐿𝑛Ti 3 Bi 4 (𝐿𝑛 = lanthanide) family.
electronic structure↗
Quantum mechanical calculations to chemical accuracy
The accuracy of current molecular-structure calculations is illustrated with examples of quantum mechanical solutions for chemical problems. Two approaches are considered: (1) the coupled-cluster singles and doubles (CCSD) with a perturbational estimate of the contribution of connected triple excitations, or CCDS(T); and (2) the multireference configuration-interaction (MRCI) approach to the correlation problem. The MRCI approach gains greater applicability by means of size-extensive modifications such as the averaged-coupled pair functional approach. The examples of solutions to chemical problems include those for C-H bond energies, the vibrational frequencies of O3, identifying the ground state of Al2 and Si2, and the Lewis-Rayleigh afterglow and the Hermann IR system of N2. Accurate molecular-wave functions can be derived from a combination of basis-set saturation studies and full configuration-interaction calculations.
Bauschlicher, Charles W., Jr.↗