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Schiff, B.; Lifson, H.; Pekeris, C. L.; Rabinowitz, P.

doi:10.1103/physrev.140.a1104

Cited by 147 publications

(32 citation statements)

References 24 publications

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“…[19] and for −1 ≤ k ≤ 2 in the P states [40] shows that our values in Table II differ from them by a maximum of 1 unit in the seventh significant figure and even that small difference is observed only for k = 2 and 3 in the 2 3 S state. Moreover, our u 4 for the 2 3 S state agrees to all five figures reported in earlier work [41].…”

Section: Densities and Momentscontrasting

confidence: 47%

Electron‐pair extracule densities for low‐lying excited states of He and Li⁺

McCarthy

Thakkar

2010

Int J of Quantum Chemistry

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ABSTRACT:The electron-pair extracule density is the probability density function for the position vector of the center-of-mass of an electron pair. Accurate calculations of spherically averaged extracule densities d(R) and their moments are reported for the 2 3 S, 2 3 P, and 2 1 P states of the helium atom and lithium cation. The computations are based on explicitly correlated wave functions with energy errors of only 2-3 nanohartrees. The role of electron correlation is probed by comparison with Hartree-Fock calculations, and Fermi correlation is probed by the differences between the singlet and triplet P states.

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Section: Densities and Momentscontrasting

confidence: 47%

Electron‐pair extracule densities for low‐lying excited states of He and Li⁺

McCarthy

Thakkar

2010

Int J of Quantum Chemistry

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“…It should be noted that similar even-odd fluctuations have also been observed in high-precision calculations using correlated basis sets [12,28,29].…”

Section: N With N Was O(n ϫ4mentioning

confidence: 72%

Convergence of an s‐Wave calculation of the He ground state

Mitroy

Bromley

Ratnavelu

2006

Int J of Quantum Chemistry

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ABSTRACT:The configuration interaction (CI) method using a large Laguerre basis restricted to ᐉ ϭ 0 orbitals is applied to the calculation of the He ground state. The maximum number of orbitals included was 60. The numerical evidence suggests that the energy converges aswhere N is the number of Laguerre basis functions. The electron-electron ␦-function expectation converges as ⌬␦ N Ϸ A/N 5/ 2 ϩ B/N 6/ 2 ϩ . . . , and the variational limit for the ᐉ ϭ 0 basis is estimated as 0.1557637174(2) a 0 3 . It was seen that extrapolation of the energy to the variational limit is dependent on the basis dimension at which the exponent in the Laguerre basis was optimized. In effect, it may be best to choose a nonoptimal exponent if one wishes to extrapolate to the variational limit. An investigation of the natural orbital asymptotics revealed the energy converged as These studies have investigated the convergence of the energy with respect to the number of partial waves included in the wave function, and also with respect to the dimension of the radial basis.It has been known since 1962 [9] that the energy converges slowly with respect to J, the maximum angular momentum of any orbital included in the CI expansion. In particular, the leading term to the energy increment is known to behave as (1) at high J. Later work [1][2][3][4]6] showed that the energy increments can be written more generally as

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“…Thus, the explicit expression for the diagram in Fig. 4b is The separation, given by (5), of the pair-function P,b, into angular and radial parts and the expression (9) for the reduced matrix elements of the momentum operator are used to derive an explicit expression for the matrix element on the right-hand side of (10 (11) p~(l,, l~-t-1,0 defined in (9). The angular factors are included in G, and represented by the angular-momentum graph in Fig.…”

Section: B L~j -Lb)j2(%l"+ L'nal")"mentioning

confidence: 99%

Isotope shifts and energies of the 1s 2p states in helium

Lindroth

Pendrill

1984

Z Physik A

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The specific mass shift (SMS) and energies of the (ls2p) ~,3p states in helium are evaluated using wave functions expressed in terms of radial "pair functions" which are obtained by numerical solution of inhomogeneous two-particle differential equations. The results obtained when including successively higher angular symmetries in the wave function indicate that the SMS converges as lm~ x for the singlet state and between 12~,~ and lm6x for the triplet state. These convergence rates are considerably slower than the l~,Sx and lm] x behaviours found for the singlet and triplet energies. The total energies, E(2~P)=-2.123835 a.u. and E(23P)=-2.133155 a.u., are about 0.00001 a.u. above the "exact" non-relativistic results obtained with perimetric coordinates and also the SMS between 3He and ~He, SMS(21P)=0.4533cm -1 and SMS(23p)---0.6356cm -1, are very close to the "exact" results.

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2P1,3,3P

Cited by 147 publications

References 24 publications

Electron‐pair extracule densities for low‐lying excited states of He and Li⁺

Electron‐pair extracule densities for low‐lying excited states of He and Li⁺

Convergence of an s‐Wave calculation of the He ground state

Isotope shifts and energies of the 1s 2p states in helium

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2P1,3,3P

Cited by 147 publications

References 24 publications

Electron‐pair extracule densities for low‐lying excited states of He and Li+

Electron‐pair extracule densities for low‐lying excited states of He and Li+

Convergence of an s‐Wave calculation of the He ground state

Isotope shifts and energies of the 1s 2p states in helium

Contact Info

Product

Resources

About

Electron‐pair extracule densities for low‐lying excited states of He and Li⁺

Electron‐pair extracule densities for low‐lying excited states of He and Li⁺