Upper bounds to the eigenvalues of the no-pair Hamiltonian

Jáuregui, R.; Bunge, Carlos F.; Ley‐Koo, E.

doi:10.1103/physreva.55.1781

Cited by 40 publications

(35 citation statements)

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“…The error due to CI by part ∆E OBI are estimated according to sensitivity analysis [18], which lead to ∆E CIBP 1 µHa. The relativistic correction contribution to both IP and EA have been estimated by carried out calculations at relativistic HartreeFock level [21] on the related atomic lowest levels 1 S, 2 P 1/2 and 3 P 0 belonging to 1 S, 2 P and 3 P states respectively. Our result for relativistic contribution to electron anity is little bit below de Oliveira et al [7] result, the reason for this dierence is due to that in de Oliveira relativistic calculation just including the spinorbit, Darwin and mass-velocity terms.…”

Section: Resultsmentioning

confidence: 99%

CI Calculations of the Ground State Ionization Potential and Electron Affinity of Aluminum

Hussein

2015

Acta Phys. Pol. A

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Nonrelativistic conguration interaction study for Al + , Al and Al − are presented, included calculations of ionization potential and electron anity of the 2 P o ground state of Al. CI calculations up to double, triple and quadrupole excitations for Al + , Al and Al − , respectively, where neon xed core is considered. Appropriate Slater type basis functions were developed suitable to recover both of core-valence and corecore correlation eect. The relativistic eect on both ionization potential and electron anity are taken into account at the relativistic HartreeFock level. The calculated electron anity is 432.811 meV which is in excellent agreement with experimental value of Sheer et al. 432.83(5) meV, whereas the calculated ionization potential is 5985.764 meV, the latter is in perfect agreement with experimental value of 5985.768 meV.

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Section: Resultsmentioning

confidence: 99%

CI Calculations of the Ground State Ionization Potential and Electron Affinity of Aluminum

Hussein

2015

Acta Phys. Pol. A

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“…This new orbital set is called a double-primitive (DP) orbital set [36]. Of course, the variational theorem holds also for the DP orbital bases.…”

Section: …22 †mentioning

confidence: 98%

“…indicating that the eigenvalues E ‡ i of relativistic CI calculations with positive-energy orbitals will always lie at or below the eigenvalues E N ¡ …2g † ‡i of the full CI matrix H DC [36], whatever choice of positive-energy orbitals is made (arbitrary h 0 ), including the choices made in connection with the no-pair Hamiltonian [12,13,37]. Note that equation (20) is independent of the speci® c form of H: it simply relates the eigenvalues of H and H ‡ .…”

Section: H DC Was Not Sick After Allmentioning

confidence: 99%

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Justification of relativistic Dirac-Hartree-Fock and configuration interaction

Bunge

Ley‐Koo²,

Jáuregui

2000

Molecular Physics

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Before knowing that the relativistic Hamiltonian H does allow the existence of bounded states (H is unbounded from below and from above), the existence of SCF and beyond SCF solutions had to be assumed as an act of faith vindicated by consistent numerical results. A recent theorem showing the existence of such bounded states furnishes a rigorous framework for the relativistic theory of electronic bounded states. IntroductionThe atomic physics community sees Charlotte Froese Fischer as the mother of Hartree± Fock methodology, both at the independent particle model (IPM) level of approximation and beyond the IPM [1, 2], without demerit of grandfather Douglas Hartree [3]. Why? For many reasons: she was the ® rst (i) to show how to handle`di cult' con® gurations [4] against prevailing scepticism, (ii) to develop e ectively convergent and ecient numerical self-consistent-® eld (SCF) procedures [5] when analytical methods were reigning supreme [6, 7], (iii) to reliably apply SCF methods beyond the IPM [1,8], when most connoisseurs thought they would not work, and (iv) to write and to make public the most used and useful computer programs for ab initio calculations of atomic structures [9, 10]. Not surprinsigly, she is now playing an important role in leading the new generations into the relativistic realm [11]. In this context, we present some recent work on the foundations of multicon® guration Dirac± Hartree± Fock theory, with special emphasis on the IPM.As one goes from the non-relativistic Schro È dinger equation into Dirac's relativistic theory of the electron, the Hamiltonian becomes unbounded: upon variation in a trial function within Hilbert space, the expectation value h D ,

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“…Needless to emphasize, SCI applies mutatis mutandis to the Dirac-Schrödinger equation, 104 and also to the BreitDirac-Schrödinger equation, 105 provided only positiveenergy orbitals are used, viz., within the no-pair Hamiltonian approximation. 106 In fact, the computer program ATMOL 54 has precisely that capability for general atomic states.…”

Section: Impact On Other Methods and Outlookmentioning

confidence: 99%

Selected configuration interaction with truncation energy error and application to the Ne atom

Bunge

2006

The Journal of Chemical Physics

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Selected configuration interaction ͑SCI͒ for atomic and molecular electronic structure calculations is reformulated in a general framework encompassing all CI methods. The linked cluster expansion is used as an intermediate device to approximate CI coefficients B K of disconnected configurations ͑those that can be expressed as products of combinations of singly and doubly excited ones͒ in terms of CI coefficients of lower-excited configurations where each K is a linear combination of configuration-state-functions ͑CSFs͒ over all degenerate elements of K. Disconnected configurations up to sextuply excited ones are selected by Brown's energy formula,with B K determined from coefficients of singly and doubly excited configurations. The truncation energy error from disconnected configurations, ⌬E dis , is approximated by the sum of ⌬E K s of all discarded Ks. The remaining ͑connected͒ configurations are selected by thresholds based on natural orbital concepts. Given a model CI space M, a usual upper bound E S is computed by CI in a selected space S, and E M = E S + ⌬E dis + ␦E, where ␦E is a residual error which can be calculated by well-defined sensitivity analyses. An SCI calculation on Ne ground state featuring 1077 orbitals is presented. Convergence to within near spectroscopic accuracy ͑0.5 cm −1 ͒ is achieved in a model space M of 1.4ϫ 10 9 CSFs ͑1.1ϫ 10 12 determinants͒ containing up to quadruply excited CSFs. Accurate energy contributions of quintuples and sextuples in a model space of 6.5ϫ 10 12 CSFs are obtained. The impact of SCI on various orbital methods is discussed. Since ⌬E dis can readily be calculated for very large basis sets without the need of a CI calculation, it can be used to estimate the orbital basis incompleteness error. A method for precise and efficient evaluation of E S is taken up in a companion paper.

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Upper bounds to the eigenvalues of the no-pair Hamiltonian

Cited by 40 publications

References 14 publications

CI Calculations of the Ground State Ionization Potential and Electron Affinity of Aluminum

CI Calculations of the Ground State Ionization Potential and Electron Affinity of Aluminum

Justification of relativistic Dirac-Hartree-Fock and configuration interaction

Selected configuration interaction with truncation energy error and application to the Ne atom

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