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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The nature of the chemical bond and the role of non-dynamical and dynamical correlation in Be2

In the spin-coupled generalized valence bond (SCGVB) description of Be2, there is a pair of electrons in highly overlapping “inner” orbitals corresponding to a traditional σ bond, but this bond is compromised by Pauli repulsion arising from its overlap with a second “outer” pair. The presence of this outer pair of electrons leads to a repulsive potential energy curve at long range and a bound, but metastable molecule at short range. To obtain further insights into the nature of the bond in Be2, we determined the non-dynamical and dynamical correlation contributions to the potential energy curve of Be2 using four different choices for the zero-order wave function: Restricted Hartree–Fock (RHF), SCGVB, valence-CASSCF(4,4), and valence-CASSCF(4,8). The SCGVB and valence-CASSCF(4,4) wave functions yield similar breakdowns of the total correlation energy, with non-dynamical correlation being the more important contribution. For the RHF and valence-CASSCF(4,8) wave functions, dynamical correlation is critical, without which the potential energy curve is purely repulsive. High accuracy calculations on the HBen−1Be–BeBen−1H molecule as a function of n (n = 1–6) suggest that the intrinsic strength of a Be–Be σ bond uncompromised by Pauli repulsion is on the order of 62–63 kcal/mol, and its length is 2.13–2.14 Å, ∼60 kcal/mol stronger and ∼0.35 Å shorter than in Be2.

Xu, Lu. T. (ORCID:0000000182064902)↗
DOE OSTI2022

Diffusion Monte Carlo approaches for studying nuclear quantum effects in fluxional molecules

Abstract Diffusion quantum Monte Carlo (DMC) provides a powerful approach for obtaining the ground state energy and wave function of molecules, ions, and molecular clusters. The approach is uniquely well suited for studies of fluxional molecules, which undergo large amplitude vibrational motions even in their ground state. In contrast to the electronic structure problem, where the wave function must be antisymmetric with respect to exchange of any pair of electrons, the wave function for the ground vibrational state is nodeless. This greatly simplifies the application of DMC for vibrational problems. Because there is not a single potential function that can be used to describe the intramolecular and intermolecular interactions in all molecular systems, most methods that are used to describe nuclear quantum effects rely on a carefully chosen zero‐order description of the molecular vibrations. In contrast, DMC calculations can be performed in Cartesian coordinates, making the DMC algorithm easily transferable between different chemical systems. In this contribution, the theory that underlies DMC will be discussed along with important considerations for performing DMC calculations. Extensions for evaluating vibrationally excited states and molecular properties are also discussed. Insights that can be obtained from DMC calculations are illustrated in the context of the protonated water clusters. This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Theoretical and Physical Chemistry > Spectroscopy

Chemistry↗
NASA NTRS2013

A T Matrix Method Based upon Scalar Basis Functions

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

wave functions↗
DOE OSTI2022

Huzinaga projection embedding for efficient and accurate energies of systems with localized spin-densities

We demonstrate the accuracy and efficiency of the restricted open-shell and unrestricted formulation of the absolutely localized Huzinaga projection operator embedding method. Restricted open-shell and unrestricted Huzinaga projection embedding in the full system basis is formally exact to restricted open-shell and unrestricted Kohn–Sham density functional theory, respectively. By utilizing the absolutely localized basis, we significantly improve the efficiency of the method while maintaining high accuracy. Furthermore, the absolutely localized basis allows for high accuracy open-shell wave function methods to be embedded into a closed-shell density functional theory environment. The open-shell embedding method is shown to calculate electronic energies of a variety of systems to within 1 kcal/mol accuracy of the full system wave function result. For certain highly localized reactions, such as spin transition energies on transition metals, we find that very few atoms are necessary to include in the wave function region in order to achieve the desired accuracy. This extension further broadens the applicability of our absolutely localized Huzinaga level-shift projection operator method to include open-shell species. Here, we apply our method to several representative examples, such as spin splitting energies, catalysis on transition metals, and radical reactions.

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

Effects of screening and pressure ionization on the electron broadening of spectral lines in dense plasmas

Collisions between electrons and radiating atoms broaden spectral absorption and emission lines in dense plasmas. High densities also introduce screening and pressure ionization effects that distort the wave functions of both bound and free electrons. In order to study how dense plasma effects influence the electron broadening of spectral lines, this paper incorporates electron wave functions from an average-atom (AA) model to calculate the linewidth of the B III 2⁢𝑝−2⁢𝑠 transition at 𝑇 = 10 eV for mass densities ranging from 𝜌 = 10 −4 to 0.4⁢ g⁡/cc. The calculation method uses the impact approximation, allowing the linewidth to be written in terms of electron-collision cross sections and an interference term. Compared to an otherwise identical calculation that uses Coulomb free wave functions, the AA method is found to modify both the cross sections and the resulting linewidth at sufficiently high density by introducing screening and pressure-ionized bound states. Screening lowers the cross sections at low energies and near electron excitation thresholds, while pressure-ionized bound states introduce resonances into the continuum. Thus, as the density increases, the relative linewidth between the AA and Coulomb calculations follows a general decrease because of screening, with sharp increases at various intervals due to pressure ionization. Finally, the AA results are also compared with a common approach to introduce screening through the interaction potential and reduced models that use the Bethe formula for the inelastic electron-collision cross sections.

electronic excitation & ionization↗
DOE OSTI2020

Large classes of quantum scarred Hamiltonians from matrix product states

Motivated by the existence of exact many-body quantum scars in the Affleck-Kennedy-Lieb-Tasaki (AKLT) chain, in this work we explore the connection between matrix product state (MPS) wave functions and many-body quantum scarred Hamiltonians. We provide a method to systematically search for and construct parent Hamiltonians with towers of exact eigenstates composed of quasiparticles on top of an MPS wave function. These exact eigenstates have low entanglement in spite of being in the middle of the spectrum, thus violating the strong eigenstate thermalization hypothesis. Using our approach, we recover the AKLT chain starting from the MPS of its ground state, and we derive the most general nearest-neighbor Hamiltonian that shares the AKLT quasiparticle tower of exact eigenstates. We further apply this formalism to other simple MPS wave functions, and derive families of Hamiltonians that exhibit AKLT-like quantum scars. As a consequence, we also construct a scar-preserving deformation that connects the AKLT chain to the integrable spin-1 pure biquadratic model. Finally, we also derive other families of Hamiltonians that exhibit types of exact quantum scars, including a $\textit{U}$(1)-invariant perturbed Potts model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

237 Np Mössbauer Isomer Shifts: A Lesson About the Balance of Static and Dynamic Electron Correlation in Heavy Element Complexes

A large set of neptunium compounds with different oxidation states (III to VII) was assembled to study the Mössbauer isomer shift by wave function calculations and better understand covalency in f-elements complexes. The contact density approach was used to calculate the isomer shift using complete active space self-consistent field (CASSCF) multiconfiguration wave functions, as well as matrix product states [from Density Matrix Renormalization Group (DMRG) algorithms] for large active spaces. Dynamic correlation effects for the isomer shifts were treated via CASPT2 energy derivatives with respect to the nuclear radius. The CASSCF calculations appear to produce different orbital overlocalization errors for low and high Np oxidation states. For compounds with low Np oxidation numbers, the errors can be attributed to the overlocalization of the 5f orbitals. For the compounds with high Np oxidation numbers, the main errors arise from an overlocalization of ligand orbitals and concomitant to weak donation bonding. Attempts to mitigate the overlocalization errors with large active spaces using DMRG were only partially successful, showing that explicit treatment of dynamic correlation is necessary for accurate predictions of Mössbauer isomer shifts. The CASPT2 calculations perform very satisfactorily. For a subset of Np compounds, both static and dynamic correlation effects were substantial. Furthermore, a rational active space selection based on orbital entanglement diagrams proved beneficial for determining the optimal reference wave function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1973

Calculation of total electron excitation cross-sections and partial electron ionization cross-sections for the elements

Computer programs were used to calculate the total electron excitation cross-section for atoms and the partial ionization cross-section. The approximations to the scattering amplitude used are as follows: (1) Born, Bethe, and Modified Bethe for non-exchange excitation; (2) Ochkur for exchange excitation; and (3) Coulomb-Born of non-exchange ionization. The amplitudes are related to the differential cross-sections which are integrated to give the total excitation (or partial ionization) cross-section for the collision. The atomic wave functions used are Hartree-Fock-Slater functions for bound states and the coulomb wave function for the continuum. The programs are presented and the results are examined.

Green, T. J.↗
DOE OSTI2021

Tensor force role in β decays analyzed within the Gogny-interaction shell model

The half-life of the famous C 14 β decay is anomalously long, with different mechanisms: the tensor force, cross-shell mixing, and three-body forces, proposed to explain the cancellations that lead to a small transition matrix element. In this study, we revisit and analyze the role of the tensor force for the β decay of C 14 as well as of neighboring isotopes. We add a tensor force to the Gogny interaction, and derive an effective Hamiltonian for shell-model calculations. The calculations were carried out in a p – s d model space to investigate cross-shell effects. Furthermore, we decompose the wave functions according to the total orbital angular momentum L in order to analyze the effects of the tensor force and cross-shell mixing. The inclusion of the tensor force significantly improves the shell-model calculations of the β -decay properties of carbon isotopes. In particular, the anomalously slow β decay of C 14 can be explained by the isospin T = 0 part of the tensor force, which changes the components of N 14 with the orbital angular momentum L = 0 , 1 , and results in a dramatic suppression of the Gamow-Teller transition strength. At the same time, the description of other nearby β decays are improved. Decomposition of wave function into L components illuminates how the tensor force modifies nuclear wave functions, in particular suppression of β -decay matrix elements. Cross-shell mixing also has a visible impact on the β -decay strength. Inclusion of the tensor force does not seem to significantly change, however, binding energies of the nuclei within the phenomenological interaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1989

General contraction of Gaussian basis sets. Part 2: Atomic natural orbitals and the calculation of atomic and molecular properties

A recently proposed scheme for using natural orbitals from atomic configuration interaction (CI) wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outmost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital (ANO) sets.

Almloef, Jan↗
NASA NTRS1990

General contraction of Gaussian basis sets. II - Atomic natural orbitals and the calculation of atomic and molecular properties

A recently proposed scheme for using natural orbitals from atomic configuration interaction wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outermost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital sets.

Almlof, Jan↗
DOE OSTI2020

Binding and excitations in Si x H y molecular systems using quantum Monte Carlo

In this work, we present high-accuracy correlated calculations of small SixHy molecular systems in both the ground and excited states. We employ quantum Monte Carlo (QMC) together with a variety of many-body wave function approaches based on basis set expansions. The calculations are carried out in a valence-only framework using recently derived correlation consistent effective core potentials. Our primary goal is to understand the fixed-node diffusion QMC errors in both the ground and excited states with single-reference trial wave functions. Using a combination of methods, we demonstrate the very high accuracy of the QMC atomization energies being within ≈0.07 eV or better when compared with essentially exact results. By employing proper choices for trial wave functions, we have found that the fixed-node QMC biases for total energies are remarkably uniform ranging between 1% and 3.5% with absolute values at most ≈0.2 eV across the systems and several types of excitations such as singlets and triplets as well as low-lying and Rydberg-like states. Our results further corroborate that Si systems, and presumably also related main group IV and V elements of the periodic table (Ge, Sn, etc), exhibit some of the lowest fixed-node biases found in valence-only electronic structure QMC calculations.

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

Discovery versus precision in nuclear physics: A tale of three scales

At least three length scales are important in gaining a complete understanding of the physics of nuclei. These are the radius of the nucleus, the average inter-nucleon separation distance, and the size of the nucleon. The connections between the different scales are examined by using examples that demonstrate the direct connection between short-distance and high-momentum transfer physics and also that significant high-momentum content of wave functions is inevitable. The nuclear size is connected via the independent-pair approximation to the nucleon-nucleon separation distance, and this distance is connected via the concept of virtuality to the EMC effect. An explanation of the latter is presented in terms of light-front holographic wave functions of QCD. The net result is that the three scales are closely related, so that a narrow focus on any given specific range of scales may prevent an understanding of the fundamental origins of nuclear properties. It is also determined that, under certain suitable conditions, experiments are able to measure the momentum dependence of wave functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation

This work explores the ability of classical electronic structure methods to efficiently represent (compress) the information content of full configuration interaction (FCI) wave functions. We introduce a benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D close-packed pyramid. To assess the ability of a computational method to produce accurate and compact wave functions, we introduce the accuracy volume, a metric that measures the number of variational parameters necessary to achieve a target energy error. Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: (i) selected configuration interaction (sCI) realized both via an a posteriori (ap-sCI) and variational selection of the most important determinants, (ii) an a posteriori singular value decomposition (SVD) of the FCI tensor (SVD-FCI), and (iii) the matrix product state representation obtained via the density matrix renormalization group (DMRG). We find that the DMRG generally gives the most efficient wave function representation for all systems, particularly in the 1D chain with a localized basis. For the 2D and 3D systems, all methods (except DMRG) perform best with a delocalized basis, and the efficiency of sCI and SVD-FCI is closer to that of DMRG. For larger analogs of the models, the DMRG consistently requires the fewest parameters but still scales exponentially in 2D and 3D systems, and the performance of SVD-FCI is essentially equivalent to that of ap-sCI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Alternative CNDOL Fockians for fast and accurate description of molecular exciton properties

CNDOL is an a priori, approximate Fockian for molecular wave functions. In this study, we employ several modes of singly excited configuration interaction (CIS) to model molecular excitation properties by using four combinations of the one electron operator terms. Those options are compared to the experimental and theoretical data for a carefully selected set of molecules. The resulting excitons are represented by CIS wave functions that encompass all valence electrons in the system for each excited state energy. The Coulomb–exchange term associated to the calculated excitation energies is rationalized to evaluate theoretical exciton binding energies. This property is shown to be useful for discriminating the charge donation ability of molecular and supermolecular systems. Multielectronic 3D maps of exciton formal charges are showcased, demonstrating the applicability of these approximate wave functions for modeling properties of large molecules and clusters at nanoscales. This modeling proves useful in designing molecular photovoltaic devices. Our methodology holds potential applications in systematic evaluations of such systems and the development of fundamental artificial intelligence databases for predicting related properties.

Chemistry↗
DOE OSTI2022

Bosonic field digitization for quantum computers

Quantum simulation of quantum field theory is a flagship application of quantum computers that promises to deliver capabilities beyond classical computing. The realization of quantum advantage will require methods that can accurately predict error scaling as a function of the resolution and parameters of the model and that can be implemented efficiently on quantum hardware. In this paper, we address the representation of lattice bosonic fields in a discretized field amplitude basis, develop methods to predict error scaling, and present efficient qubit implementation strategies. A low-energy subspace of the bosonic Hilbert space, defined by a boson occupation number cutoff, can be represented with exponentially good accuracy by a low-energy subspace of a finite-size Hilbert space. The finite representation construction and the associated errors are directly related to the accuracy of the Nyquist-Shannon sampling and the finite Fourier transforms of the boson number states in the field and the conjugate-field bases. We analyze the relation between the boson mass, the discretization parameters used for wave function sampling, and the finite representation size. Numerical simulations of small size Φ 4 problems demonstrate that the boson mass optimizing the sampling of the ground state wave function is a good approximation to the optimal boson mass yielding the minimum low-energy subspace size. However, we find that accurate sampling of general wave functions does not necessarily result in accurate representation. Finally, we develop methods for validating and adjusting the discretization parameters to achieve more accurate simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1992

Homogeneous quantum electrodynamic turbulence

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Shebalin, John V.↗
DOE OSTI2023

Constraint of pionless EFT using two-nucleon spectra from lattice QCD

Finite-volume pionless effective field theory (FVEFT π/ ) at next-to-leading order (NLO) is used to analyze the two-nucleon lattice QCD spectrum of Ref. [1], performed at quark masses corresponding to a pion mass of approximately 800 MeV. Specifically, the effective theory is formulated in finite volume, and variational sets of wave functions are optimized using differential programming. Using these wave functions projected to the appropriate finite-volume symmetry group, variational bounds from FVEFT π/ are obtained for the ground state, as well as excited states. By comparison with the lattice QCD GEVP spectrum, different low energy constants (LECs) are constrained. Furthermore, relativistic corrections are incorporated, allowing for the s-d-wave mixing term in the deuteron channel.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗