Optimized central potentials for atomic ground-state wavefunctions

Aashamar, K; Luke, T M; Talman, James J.

doi:10.1016/0092-640x(78)90019-0

Cited by 144 publications

(68 citation statements)

References 11 publications

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“…Instead a certain compromise between the number of free parameters and the accuracy at the effective potential framework has been found. For example when using the single configuration 1s 2 2s 2 to describe the ground state of the Be atom, the effective potential wave function used here provides an energy of −14.57235 au to be compared with the optimized effective potential results −14.57245 au and −14.57256 au reported in [23] and [24] respectively and with the Hartree-Fock value −14.57302 au. In the case of a multi configuration wave function built from the linear combination of the configurations 1s 2 2s 2 and 1s 2 2p 2 that takes into account the near degeneracy effect and constitutes the complete active space wave function for this atom, the optimized effective potential energy obtained by us is −14.61556 au while the exact Multi Configuration Hartree Fock (MCHF) value with these two configurations is −14.61685 au [25].…”

Section: Wave Functionmentioning

confidence: 99%

“…This is a mean field approximation to the many electron problem based on finding the best local one-body potential minimizing the total energy, which is expressed as an orbital functional as in the Hartree-Fock approach. This method was first proposed by Slater [21] as a simplification of the Hartree-Fock equations and further developed and applied to atomic problems by Talman and coworkers [22,23]. The trial wave function is a Slater determinant with single-particle wave functions calculated from a certain effective potential that is assumed to be central.…”

Section: Wave Functionmentioning

confidence: 99%

“…The minimum condition on the effective potential leads to a set of non-linear coupled integro-differential equations involving the potential and the orbitals. They can be solved by means of a self-consistent procedure just like in the Hartree-Fock method by using either numerical-grid techniques [22,23] or by expanding the effective potential in a finite basis set that guarantees the fulfillment of the correct asymptotic behavior [24].…”

Section: Wave Functionmentioning

confidence: 99%

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Excited states of beryllium atom from explicitly correlated wave functions

Gálvez

Buendı́a

Sarsa

2002

The Journal of Chemical Physics

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A study of the first excited states of beryllium atom starting from explicitly correlated wave functions is carried out. Several properties are obtained and discussed focusing on the analysis of the Hund's rules in terms of the single-particle and electron pair intracule and extracule densities. A systematic study of the differences on the electronic distributions of the singlet and triplet states is carried out. The trial wave function used to describe the different bound states consists of a generalized Jastrowtype correlation factor times a configuration interaction model wave function. This model wave function has been fixed by using a generalization of the optimized effective potential method to deal with multiconfiguration wave functions. The optimization of the wave function and the calculation of the different quantities is carried out by means of the Variational Monte Carlo method.

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Section: Wave Functionmentioning

confidence: 99%

Section: Wave Functionmentioning

confidence: 99%

Section: Wave Functionmentioning

confidence: 99%

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Excited states of beryllium atom from explicitly correlated wave functions

Gálvez

Buendı́a

Sarsa

2002

The Journal of Chemical Physics

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“…In the OEP method an additional constraint is imposed on the variational problem: the orbitals must satisfy a single-particle equation with a certain local potential that is the same for all the electrons. The OEP was reformulated [11] and implemented [12,13] by numerically solving the integral equation (NOEP). An alternative methodology for solving the OEP equations was proposed elsewhere [14][15][16][17] based on an analytical parameterization of the potential (POEP).…”

Section: Introductionmentioning

confidence: 99%

New analytical independent-particle model potential for atoms

Yu¹,

Sun

2010

Open Physics

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Abstract:A new analytical, independent-particle model potential with four shell-independent parameters is proposed, which is suitable for high, medium, and low Z atoms. The four parameters are determined for 101 atoms from Li to Lr by fitting the results of the X method found in the literature. The average fitting error 0.675% of the new potential for the 101 atoms is far better than 3.92% of the widely used Green's potential. The radial Schrödinger equation with the new potential is solved by using Numerov's numerical method for 7 typical atoms: Ne, Ca, Zn, Zr, Sn, Yb, and Th. The energy eigenvalues, radial wave functions, and atomic ground-state energy are in good agreement with the results of the X method. The new potential here shows greater flexibility and better accuracy compared with the Green's potential. PACS (2008):31.15.B-. Keywords:atomic structure • independent-particle model • energy eigenvalues © Versita Sp. z o.o.

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“…This gives rise to a linear integral equation in the effective potential [4,5] whose solution provides the optimized effective potential. This equation was first solved by Talman and coworkers by using a numerical scheme [5] and a complete tabulation for the ground state of the atoms Li through Rd was reported [6].…”

Section: Introductionmentioning

confidence: 99%