High‐precision Hy–CI variational calculations for the ground state of neutral helium and helium‐like ions

Sims, James S.; Hagstrom, Stanley A.

doi:10.1002/qua.10344

Cited by 73 publications

(97 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Quadruple precision was used throughout the calculations. As in our recent work [26,[28][29][30], MPI [31] was used to parallelize the code. The number of processes used varied from 12 to 48 with 32 being typical.…”

Section: Methods Of Calculationmentioning

confidence: 99%

Hylleraas-configuration-interaction study of the1Sground state of neutral beryllium

Sims

Hagstrom

2011

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Methods Of Calculationmentioning

confidence: 99%

Hylleraas-configuration-interaction study of the1Sground state of neutral beryllium

Sims

Hagstrom

2011

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

show abstract

“…2, the error of the approximation of the lowest eigenvalue with respect to the degrees of freedom is shown. The reference value is obtained from [39]. The asymptotic convergence behavior starts around 10 5 and is determined numerically to be approximately 0.465.…”

Section: Lemma 15mentioning

confidence: 99%

“…In addition, the regularity assumptions Fig. 2 Error of the eigenvalue approximation in atomic units of the lowest eigenvalue of helium with respect to the degrees of freedom, where the reference value is taken from [39]. The approximation is calculated by a Galerkin discretization using adaptively refined anisotropic sparse grids based on linear prewavelets [8].…”

Section: Lemma 15mentioning

confidence: 99%

Wavelet Approximation in Weighted Sobolev Spaces of Mixed Order with Applications to the Electronic Schrödinger Equation

Zeiser

2011

Constr Approx

View full text Add to dashboard Cite

We study the approximation of functions in weighted Sobolev spaces of mixed order by anisotropic tensor products of biorthogonal, compactly supported wavelets. As a main result, we characterize these spaces in terms of wavelet coefficients, which also enables us to explicitly construct approximations. In particular, we derive approximation rates for functions in exponentially weighted Sobolev spaces discretized on optimized general sparse grids. Under certain regularity assumptions, the rate of convergence is independent of the number of dimensions. We apply these results to the electronic Schrödinger equation and obtain a convergence rate which is independent of the number of electrons; numerical results for the helium atom are presented.

show abstract

“….). This method was used by several authors in CI and Hy-CI calculations on helium [23], lithium [12,24] and beryllium [25] atoms. The method allows large wave function expansions, but it needs relatively short computational times (from several hours to several days).…”

Section: Computational Aspectsmentioning

confidence: 99%

Configuration interaction calculations on the ²P ground state of boron atom and C⁺ using Slater orbitals

Ruiz

Rojas

Chicón

et al. 2011

Int J of Quantum Chemistry

View full text Add to dashboard Cite

Configuration Interaction (CI) calculations on the ground 2 P state of boron atom are presented using a wave function expansion constructed with L-S eigenfunction configurations of s-, p-, and d-Slater orbitals. Two procedures of optimization of the orbital exponents have been investigated. First, CI(SD) calculations including few types of configurations and full optimization of the orbital exponents led to the energy −24.63704575 a.u. Second, full-CI (FCI) calculations including a large number of configuration types using a fixed set of orbital exponents for all configurations gave −24.63405222 a.u. using the basis [4s3p2d] and 2157 configurations, and to an improved result of −24.64013999 a.u. for 3957 configurations and a [5s4p3d] basis. This last result is better than earlier calculations of Schaefer and Harris (Phys Rev 1968, 167, 67), and compares well with the recent ones from Froese Fischer and Bunge (personal communication). In addition, using the same wave functions, CI calculations of the boron isoelectronic ion C + have been performed obtaining an energy of −37.41027598 a.u.

show abstract

High‐precision Hy–CI variational calculations for the ground state of neutral helium and helium‐like ions

Abstract: Hylleraas-configuration

Cited by 73 publications

References 37 publications

Hylleraas-configuration-interaction study of the1Sground state of neutral beryllium

Hylleraas-configuration-interaction study of the1Sground state of neutral beryllium

Wavelet Approximation in Weighted Sobolev Spaces of Mixed Order with Applications to the Electronic Schrödinger Equation

Configuration interaction calculations on the ²P ground state of boron atom and C⁺ using Slater orbitals

Contact Info

Product

Resources

About

High‐precision Hy–CI variational calculations for the ground state of neutral helium and helium‐like ions

Abstract: Hylleraas-configuration

Cited by 73 publications

References 37 publications

Hylleraas-configuration-interaction study of the1Sground state of neutral beryllium

Hylleraas-configuration-interaction study of the1Sground state of neutral beryllium

Wavelet Approximation in Weighted Sobolev Spaces of Mixed Order with Applications to the Electronic Schrödinger Equation

Configuration interaction calculations on the 2P ground state of boron atom and C+ using Slater orbitals

Contact Info

Product

Resources

About

Configuration interaction calculations on the ²P ground state of boron atom and C⁺ using Slater orbitals