An accurate few‐parameter ground state wave function for the lithium atom

Guevara, Nicolais L.; Harris, Frank E.; Turbiner, A. V.

doi:10.1002/qua.22217

Cited by 23 publications

(43 citation statements)

References 15 publications

(33 reference statements)

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“…Among the three, there is a dramatic difference in energy (0.01 hartree) that depends solely on the presence of prefactors. The energy minima for these three functions were evaluated and minimized numerically by Guevara et al 23. The results were similar to those reported here, thereby confirming the accuracy of the analytical evaluation.…”

Section: Resultssupporting

confidence: 86%

“…For Ps 2 this is a reasonable basis, but it not optimum for Li, where the zero‐order electronic configuration is of the form 1s 2 2s, and a good description of the 2s orbital would be expected to require pre‐exponential term(s) linear in r . An initial study that included such terms was carried out by Guevara et al by a method in which the necessary six‐dimensional integrals were evaluated numerically 23; it showed the importance of the pre‐exponential factors.…”

Section: Introductionmentioning

confidence: 99%

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Few‐parameter exponentially correlated wavefunctions for the ground state of lithium

Albert

Guevara

Sabin

et al. 2009

Int J of Quantum Chemistry

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ABSTRACT:Compact, but relatively accurate wavefunctions for the ground state of the Li atom were obtained through the use of a limited basis of exponentially correlated functions with optimized nonlinear parameters. In contrast to our earlier work, the basis contains pre-exponential factors that improve the rate of convergence of the basis-set expansion. The matrix elements needed in the present work were evaluated analytically using recursive methods reported recently by one of us; a check on the programming was provided by comparison with numerical evaluations carried out by Turbiner and Guevara. The rate of convergence of the expansion is compared with those of Hylleraas-basis computations, and a comparison is also made with exponentially correlated studies of He-like systems.

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Section: Resultssupporting

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Few‐parameter exponentially correlated wavefunctions for the ground state of lithium

Albert

Guevara

Sabin

et al. 2009

Int J of Quantum Chemistry

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“…In order to check consistency we found that (15) at the critical point Z = Z cr,3e reproduces the ground-state energy of the 2e (14) where all displayed digits assumed to be correct and E (fit) 3e from the fit (15). system E 2e in 6 s.d.…”

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confidence: 94%

Heliumlike and lithiumlike ionic sequences: Critical charges

Guevara

Turbiner

2011

Phys. Rev. A

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In nonrelativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge Z and two-three electrons: (Z,e,e) and (Z,e,e,e). It is shown that in both cases the total energy curve in Z is smooth, without any visible irregularities. Thus, for both systems the physical integer charges Z = 1, 2, . . . do not play a distinguished role as would be associated with charge quantization. By definition, a critical charge Z cr is a charge which separates a domain of the existence of bound states from a domain of unbound ones (continuum). For both systems the critical charges are found, Z cr,2e = 0.910850 and Z cr,3e = 2.0090, respectively. Based on numerical analysis, the Puiseux expansion in fractional powers of (Z − Z cr ) is constructed for both systems. Our results indicate the existence of a square-root branch point singularity at Z cr with exponent 3/2. A connection between the critical charge and the radius of convergence of 1/Z expansion is briefly discussed.

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“…As for the lithium atom in its ground state an attempt was already made to find a compact function in the form similar to Hylleraas function ) taking the (anti)symmetrized product of six (modified by screening) Coulomb Orbitals, see Reference 10; recently, it was extended to the Li‐like system at Z > 3 . 3 However, the goal of describing the domain of applicability of QMCC for the Li‐like three‐electronic sequence was not reached.…”

Section: Introductionmentioning

confidence: 99%

Ultra‐compact accurate wave functions for He‐like and Li‐like iso‐electronic sequences and variational calculus: I. Ground state

Turbiner

Vieyra

Valle

et al. 2020

Int J of Quantum Chemistry

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Several ultra‐compact accurate wave functions in the form of generalized Hylleraas‐Kinoshita functions and Guevara‐Harris‐Turbiner functions, which describe the domain of applicability of the Quantum Mechanics of Coulomb Charges (QMCC), for the ground state energies (4‐5 significant digits [s.d.]) of He‐like and Li‐like iso‐electronic sequences in the static approximation with point‐like, infinitely heavy nuclei are constructed. It is shown that for both sequences the obtained parameters can be fitted in Z by simple smooth functions: in general, these parameters differ from the ones emerging in variational calculations. For the He‐like two‐electron sequence the approximate expression for the ground state function, which provides absolute accuracy for the energy ∼10−3 a.u. and the same relative accuracies ∼10−2 to 10−3 for both the cusp parameters and the six expectation values, is found. For the Li‐like three‐electron sequence the most accurate ultra‐compact function taken as the variational trial function provides absolute accuracy for energy ∼10−3 a.u., 2 to 3 s.d. for the electron‐nuclear cusp parameter for Z ≤ 20 and 3 s.d. for the two expectation values for Z = 3.

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An accurate few‐parameter ground state wave function for the lithium atom

Cited by 23 publications

References 15 publications

Few‐parameter exponentially correlated wavefunctions for the ground state of lithium

Few‐parameter exponentially correlated wavefunctions for the ground state of lithium

Heliumlike and lithiumlike ionic sequences: Critical charges

Ultra‐compact accurate wave functions for He‐like and Li‐like iso‐electronic sequences and variational calculus: I. Ground state

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