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Results for “Coulomb integral”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A tight distance-dependent estimator for screening three-center Coulomb integrals over Gaussian basis functions

A new estimator for three-center two-particle Coulomb integrals is presented. Our estimator is exact for some classes of integrals and is much more efficient than the standard Schwartz counterpart due to the proper account of distance decay. Although it is not a rigorous upper bound, the maximum degree of underestimation can be controlled by two adjustable parameters. We also give numerical evidence of the excellent tightness of the estimator. The use of the estimator will lead to increased efficiency in reduced-scaling one- and many-body electronic structure theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Integrated Coulomb Blockade Thermometry for Quantum Computing

In our work we present on-chip thermometry concept aimed at improving temperature control during quantum measurements. The key issue addressed is lack of precise temperature monitoring, especially considering the unavoidable thermal resistance between the qubits’ chip and mixing plate of dilution refrigerator. The suggested solution includes a Coulomb Blockade Thermometer (CBT) based on an array of intrinsically normal-conducting tunnel junctions, currently developed at Aalto University. This is a practical solution for superconducting qubit systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Convergence of Feynman integrals in Coulomb gauge QCD

At 2-loop order, Feynman integrals in the Coulomb gauge are divergent over the internal energy variables. Nevertheless, it is known how to calculate the effective action, provided that the external gluon fields are all transverse. We show that, for the two-gluon Greens function as an example, the method can be extended to include longitudinal external fields. The longitudinal Greens functions appear in the BRST identities. As an intermediate step, we use a flow gauge, which interpolates between the Feynman and Coulomb gauges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Adaptive time-stepping Monte Carlo integration of Coulomb collisions

Here, we report an accessible and robust tool for evaluating the effects of Coulomb collisions on a test particle in a plasma that obeys Maxwell–Jüttner statistics. The implementation is based on the Beliaev–Budker collision integral which allows both the test particle and the background plasma to be relativistic. The integration method supports adaptive time stepping, which is shown to greatly improve the computational efficiency. The Monte Carlo method is implemented for both the three-dimensional particle momentum space and the five-dimensional guiding center phase space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Numerical evaluation of two-center integrals over Slater type orbitals

Slater Type Orbitals (STOs) which one of the types of exponential type orbitals (ETOs) are used usually as basis functions in the multicenter molecular integrals to better understand physical and chemical properties of matter. In this work, we develop algorithms for two-center overlap and two-center two-electron hybrid and Coulomb integrals which are calculated with help of translation method for STOs and some auxiliary functions by V. Magnasco’s group. We use Mathematica programming language to produce algorithms for these calculations. Numerical results for some quantum numbers are presented in the tables. Consequently, we compare our obtained numerical results with the other known literature results and other details of evaluation method are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1986

Analytic evaluation of two-center molecular integrals

By using the Fourier-transform technique, the explicit expressions for the one-electron - two-center overlap integrals of Slater-type atomic orbitals up to 3d are derived. The final expressions are analytic, simple, and independent of local coordinates. Furthermore, they do not contain the nonclosed-form of exponential integrals which were presented in expressions given in earlier work. It is shown that the two-electron - two-center Coulomb integrals, as well as the hybrid integrals, can simply be expressed in terms of these integrals. The numerical instability arising from the situation in which the exponents of the two orbitals are almost equal is discussed, and a solution for this problem based on a Taylor-series expansion of the integral is suggested.

Tai, H.↗
DOE OSTI2015

A novel Gaussian-Sinc mixed basis set for electronic structure calculations

A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree–Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the “localized” and “delocalized” regions. A basis set for each region is combined to make a new basis methodology—a lattice of orthonormal sinc functions is used to represent the “delocalized” regions and the atom-centered Gaussian functions are used to represent the “localized” regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definable and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree–Fock energies for atoms up to neon, the diatomic systems H{sub 2}, O{sub 2}, and N{sub 2}, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A systematic way for the cost reduction of density fitting methods

We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of three-center two-electron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of the computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of three-center Coulomb integrals is a bottleneck.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1967

Physics

Singlet-D atomic oxygen reaction with alkanes, Coulomb integral of continuum functions, and rigid motions in conformal space-time

ALKANE↗
DOE OSTI2024

GPU-Accelerated Solution of the Bethe–Salpeter Equation for Large and Heterogeneous Systems

We present a massively parallel GPU-accelerated implementation of the Bethe–Salpeter equation (BSE) for the calculation of the vertical excitation energies (VEEs) and optical absorption spectra of condensed and molecular systems, starting from single-particle eigenvalues and eigenvectors obtained with density functional theory. The algorithms adopted here circumvent the slowly converging sums over empty and occupied states and the inversion of large dielectric matrices through a density matrix perturbation theory approach and a low-rank decomposition of the screened Coulomb interaction, respectively. Further computational savings are achieved by exploiting the nearsightedness of the density matrix of semiconductors and insulators to reduce the number of screened Coulomb integrals. We scale our calculations to thousands of GPUs with a hierarchical loop and data distribution strategy. The efficacy of our method is demonstrated by computing the VEEs of several spin defects in wide-band-gap materials, showing that supercells with up to 1000 atoms are necessary to obtain converged results. We discuss the validity of the common approximation that solves the BSE with truncated sums over empty and occupied states. In conclusion, we then apply our GW-BSE implementation to a diamond lattice with 1727 atoms to study the symmetry breaking of triplet states caused by the interaction of a point defect with an extended line defect.

Absorption spectra↗
DOE OSTI2024

Stress Field Dynamics and Fault Slip Potential in the Paradox Basin

Abstract The Paradox Basin, straddling Utah, Colorado, Arizona, and New Mexico is characterized by an intricate amalgamation of evaporites and clastic layers and is dominated by prominent salt walls and related subsurface structures. Our research offers a new examination of the stress distribution across the basin, deriving from continuous and discrete stress measurements conducted in boreholes in the region and focal mechanism analysis, emphasizing variations over salt structures. Integrating Coulomb failure criteria with probabilistic methods, we assess potential fault movements resulting from fluid pressure alterations. Our approach provides a comprehensive understanding of the Paradox Basin's state of stress, showing a continuous change of the maximum horizontal stress orientation from N‐S at the Wasatch Fault Zone to WNW‐ESE in the northern part of the Paradox Basin and to WSW‐ENE in the southern part of the basin. Further East, into the Colorado Plateau and the Uncompahgre Uplift, the S H max orientation becomes E‐W. Decoding stress orientation dynamics has enabled critical insights into fault slip potential, especially in the basin's northern region. The salt wall faults are less likely to slip, and the Paradox Formation's evaporite and clastic rock sequence can serve as a potential low seismic risk target for carbon storage and hydrocarbon extraction.

Geochemistry & Geophysics↗
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 OSTI2015

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

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

Stochastic resolution of identity second-order Matsubara Green’s function theory

We create a stochastic resolution of identity representation to the second-order Matsubara Green’s function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/ contractions, which reduces the computational cost from O(N 5 ) to O(N 3 ) (with N being the number of atomic orbitals). Currently, the method can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 10 3 electrons and more.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗