Complete supermultiplet structures for the doubly excited intrashell resonances of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>associated with the H (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>, 3, and 4) thresholds

Jiao, Li Guang; Ho, Yew Kam

doi:10.1103/physreva.89.052511

Cited by 9 publications

(4 citation statements)

References 57 publications

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“…Each group of STOs shares a single value of variational parameter ξ in the exponent, which means that we have only two variational parameters in the basis set. The use of k max = 0 in equation ( 2) simply reduces the HyCI to the conventional STOCI basis set [34,35]. In practical calculations, the use of k max = 1 acquires a good balance between the computational efficiency and desired accuracy due to the numerical instability caused by the possible linearly dependent problem.…”

Section: Theoretical Foundation Of the Hyci Basis Setmentioning

confidence: 99%

Modeling the behavior of two-electron atom at critical nuclear charge

Zheng¹,

Jiao²,

Liu³

et al. 2022

J. Phys. B: At. Mol. Opt. Phys.

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The expectation values of radial and angular quantities for two-electron atoms at the critical nuclear charge where the ground state ceases to exist are calculated employing the Hylleraas-conﬁguration interaction basis functions. The radial quantities achieve better convergence than previous predictions and accurate angular quantities are reported for the ﬁrst time. Based on these quantities, the geometric structure of the system is examined to support the criteria that the critical behavior of the system can be modeled by the inner and outer electrons separately. The work of King et al. [Phys. Rev. A 93 022509 (2016)] has shown that the inner-electron probability density distribution closely resembles that of a hydrogenic atom. Here we further show that the outer electron can be reasonably modeled by a shifted exponential polarization potential with soft truncation in the short range. The model potential proposed here reproduces very well the radial expectation value of the outer electron as well as the peak position, maximum magnitude, and long-range asymptotic behavior of the outer-electron radial density distribution.

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Section: Theoretical Foundation Of the Hyci Basis Setmentioning

confidence: 99%

Modeling the behavior of two-electron atom at critical nuclear charge

Zheng¹,

Jiao²,

Liu³

et al. 2022

J. Phys. B: At. Mol. Opt. Phys.

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“…The hydrogen STO basis set, which is used for all the H 2 interatomic distances up to dissociation, is composed of 13p11d9f5g1h functions. For the H − system (2p2p, 3 P e ), this basis set yields an electronic energy of −0.1253542 E h with an error of 1 × 10 −6 E h with respect to the best available results . As for the He atom, better results can be achieved by extending the basis set to higher n ℓ functions, but since the focus is not on the atom, this basis set seems to be adequate to describe the molecule (see next section).…”

Section: Computational Detailsmentioning

confidence: 99%

Unexpected properties of non‐autoionizing doubly excited states of the H₂ molecule

Corongiu

2016

Int J of Quantum Chemistry

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We present accurate calculations of the non‐autoionizing Σ1,3g− and Σ1,3u− doubly excited states of the H2 molecule using full configuration interaction with Hartree–Fock molecular orbitals and Heitler–London atomic orbitals. We consider the united atom configurations from He(2p2p) up to He(2p8g) and dissociation products from H2(2p + 2p) up to H2(2p + 6ℓ). Born–Oppenheimer calculations are carried out with extended and optimized Slater‐type orbitals for a total of 40 states, 10 for each symmetry, covering the internuclear distances from the united atom to dissociation, which, for some states, is reached beyond 100 a0. Occurrences of repulsive states cleanly interlaced between bound states with many vibrational levels are reported. Some of the potential minima are deep enough to accommodate many vibrational levels (up to 50). Noteworthy large equilibrium minima, like Req = 46.0 a0 in the Σ3u− state dissociating as (2p + 6h) and with 18 vibrational levels. The occurrence of vertical excitations from the singly excited manifolds is analyzed. Several states present double minima generated by avoided crossings, some with a strong ionic character. © 2016 Wiley Periodicals, Inc.

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“…Those nonorthogonal bases which can be approximately “complete” by a large number of basis functions are more frequently used in the atomic and molecular structure calculations. In the framework of configuration interaction (CI) approach, the nonorthogonal basis set can be constructed by the Slater‐type orbitals (STOs), the Gaussian‐type orbitals, the Coulomb Sturmian functions as well as the explicitly correlated Hylleraas‐like basis functions …”

Section: Introductionmentioning

confidence: 99%

Application of Löwdin's canonical orthogonalization method to the Slater-type orbital configuration-interaction basis set

Jiao

2015

Int. J. Quantum Chem.

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We apply Löwdin's canonical orthogonalization method to investigate the linearly dependent problem arising from the variational calculation of atomic systems using Slater‐type orbital configuration‐interaction (STO‐CI) basis functions. With a specific arithmetic precision used in numerical computations, the nonorthogonal STO‐CI basis is easily linearly dependent when the number of basis functions is sufficiently large. We show that Löwdin's canonical orthogonalization method can successfully overcome such problem and simultaneously reduce the dimension of basis set. This is illustrated first through an S‐wave model He atom, and then the real two‐electron atoms in both the ground and excited states. In all of these calculations, the variational bound state energies of the two‐electron systems are obtained in reasonably high accuracy using over‐redundant STO‐CI bases, however, without using extended high‐precision technique. © 2015 Wiley Periodicals, Inc.

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Complete supermultiplet structures for the doubly excited intrashell resonances ofH−associated with the H (N=2, 3, and 4) thresholds

Cited by 9 publications

References 57 publications

Modeling the behavior of two-electron atom at critical nuclear charge

Modeling the behavior of two-electron atom at critical nuclear charge

Unexpected properties of non‐autoionizing doubly excited states of the H₂ molecule

Application of Löwdin's canonical orthogonalization method to the Slater-type orbital configuration-interaction basis set

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Complete supermultiplet structures for the doubly excited intrashell resonances ofH−associated with the H (N=2, 3, and 4) thresholds

Cited by 9 publications

References 57 publications

Modeling the behavior of two-electron atom at critical nuclear charge

Modeling the behavior of two-electron atom at critical nuclear charge

Unexpected properties of non‐autoionizing doubly excited states of the H2 molecule

Application of Löwdin's canonical orthogonalization method to the Slater-type orbital configuration-interaction basis set

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Product

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Unexpected properties of non‐autoionizing doubly excited states of the H₂ molecule