One-Center <i>rij</i> Integrals Over Slater-Type Orbitals

Sims, James S.; Hagstrom, Stanley A.

doi:10.1063/1.1675567

Cited by 91 publications

(73 citation statements)

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“…Some 50 years after his death, the Hylleraas Symposium 13 the combined CI and Hylleraas (CI-Hyl) methods, have been proposed for the study of multielectron atoms and diatomic molecules. [14][15][16][17][18][19][20][21] However, these expansions require the computations of difficult integrals involving products of correlation factors such as r µ 12 , r µ 12 r ν 13 , r µ 12 r ν 13 r λ 23 , r µ 12 r ν 13 r λ 14 , and so on. The complexity of these integrals has hindered applications to many-electronic and polyatomic systems, especially for the use of Slater-type orbitals.…”

Section: Introductionmentioning

confidence: 99%

Perspective: Explicitly correlated electronic structure theory for complex systems

Grüneis

Hirata

Ohnishi

et al. 2017

The Journal of Chemical Physics

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The explicitly correlated approach is one of the most important breakthroughs in ab initio electronic structure theory, providing arguably the most compact, accurate, and efficient ansatz for describing the correlated motion of electrons. Since Hylleraas first used an explicitly correlated wave function for the He atom in 1929, numerous attempts have been made to tackle the significant challenges involved in constructing practical explicitly correlated methods that are applicable to larger systems. These include identifying suitable mathematical forms of a correlated wave function and an efficient evaluation of many-electron integrals. R12 theory, which employs the resolution of the identity approximation, emerged in 1985, followed by the introduction of novel correlation factors and wave function ansätze, leading to the establishment of F12 theory in the 2000s. Rapid progress in recent years has significantly extended the application range of explicitly correlated theory, offering the potential of an accurate wave-function treatment of complex systems such as photosystems and semiconductors. This perspective surveys explicitly correlated electronic structure theory, with an emphasis on recent stochastic and deterministic approaches that hold significant promise for applications to large and complex systems including solids. Published by AIP Publishing. [http://dx

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Section: Introductionmentioning

confidence: 99%

Perspective: Explicitly correlated electronic structure theory for complex systems

Grüneis

Hirata

Ohnishi

et al. 2017

The Journal of Chemical Physics

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“…11*19, 24 These new multicenter two-electron integrals, our main concern in this article, are of the three following different types…”

Section: Two-electron Integrals In the Hylleraas-ci Methodsmentioning

confidence: 99%

The Hylleraas‐CI method in molecular calculations: Two‐electron integrals

Largo

Clementi

1987

J Comput Chem

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In the Hylleraas-CI method, first proposed by Sims and Hagstrom, correlation factors of the type r& are included into the configurations of a CI expansion. The computation of the matrix elements requires the evaluation of different two-, three-, and four-electron integrals. In this article we present formulas for the two-electron integrals over Cartesian Gaussian functions, the most used basis functions in molecular calculations. Most of the integrals have been calculated analytically in closed form (some of them in terms of the incomplete Gamma function), but in one case a numerical integration is required, although the interval for the integration is finite and the integrand well-behaved. We have also reported on partial and preliminary computations for the H1 molecule using our four-center general formulas; a basis set of s-andp-type functions yielded at R = 1.4001 A an energy of -1.174380 8.u. to be compared with Kolos and Wolniewicz value of -1.174475.

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“…The operatorÔ(L 2 ) projects over the proper spatial space, so that each configuration is eigenfunction of the square of the angular momentum operatorL 2 . In this work instead to use the projection technique, theL 2 eigenfunctions are constructed a priori.Â is the five-particle antisymmetrization operator, and χ is the spin eigenfunction:…”

Section: Theorymentioning

confidence: 99%

“…Resonances are quasi-bound states that decay through autoionizing or predissociative mechanisms [40,41]. 2 P resonances have been predicted by Kurtz and Öhrn [42,43]. The resonance energy is defined as the difference between the anion and the neutral atom.…”

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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

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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.

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One-Center rij Integrals Over Slater-Type Orbitals

Cited by 91 publications

References 15 publications

Perspective: Explicitly correlated electronic structure theory for complex systems

Perspective: Explicitly correlated electronic structure theory for complex systems

The Hylleraas‐CI method in molecular calculations: Two‐electron integrals

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

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One-Center rij Integrals Over Slater-Type Orbitals

Cited by 91 publications

References 15 publications

Perspective: Explicitly correlated electronic structure theory for complex systems

Perspective: Explicitly correlated electronic structure theory for complex systems

The Hylleraas‐CI method in molecular calculations: Two‐electron integrals

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

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Product

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