Improved Le Sech wavefunctions for two-electron atomic systems

Singh, Rabeet; Harbola, Manoj K.

doi:10.1016/j.cplett.2015.09.040

Cited by 10 publications

(17 citation statements)

References 28 publications

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“…For both H

^{-}

and He atoms, its value is close to the experimental number which is

- 0.0277 au

for H

^{-}

and

- 0.9038 au

for He. For

α = 1

parameters obtained with the van Leeuwen–Barends calculations are the same as those obtained in our previous work …”

Section: Resultssupporting

confidence: 78%

“…For atoms and ions in the He isoelectronic series, the external potential is

- \frac{Z}{r}

and an accurate wavefunction for

α = 1

is given as

Ψ^{α = 1} ({\overset{r}{true}}_{1}, {\overset{r}{true}}_{2}) = ϕ ({\overset{r}{true}}_{1}) ϕ ({\overset{r}{true}}_{2}) [\cosh a r_{1} + \cosh a r_{2}]

[1 + 0.5 r_{12} e^{- b r_{12}}]

where

ϕ (\overset{r}{true})

is obtained by solving the Equation with

α = 1

and

Δ v_{ext}^{α} = 0

. The wavefunction in Equation is a generalization of the Le Sech wavefunction where

ϕ (\overset{r}{true}) = e^{- Z r}

and provides flexibility in

ϕ (\overset{r}{true})

so that the wavefunction can be varied for different values of

α

to fit a given density.…”

Section: Resultsmentioning

confidence: 99%

“…[ ] and [ ], a simple and compact semianalytic wavefunction is constructed for all values of

α

. This wavefunction is expressed as a product of orbitals and a correlation factor and is given as

Ψ^{α} ({\overset{r}{true}}_{1}, {\overset{r}{true}}_{2}) = ϕ ({\overset{r}{true}}_{1}) ϕ ({\overset{r}{true}}_{2}) f^{α} (r_{1}, r_{2}, r_{12})

where the correlation factor

f^{α} (r_{1}, r_{2}, r_{12}) = (1 + 0.5 α r_{12})

for the Hookium atom, and

f^{α} (r_{1}, r_{2}, r_{12}) = (\cosh a r_{1} + \cosh a r_{2}) (1 + 0.5 α r_{12} e^{- b r_{12}})

for atoms. In the expressions above

{\overset{r}{true}}_{1}

and

{\overset{r}{true}}_{2}

are the coordinates of the two electrons,

r_{12} = | {\overset{r}{true}}_{1} - {\overset{r}{true}}_{2} |

and

…”

Section: Introductionmentioning

confidence: 99%

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Study of adiabatic connection in density functional theory with an accurate wavefunction for two‐electron spherical systems

Singh

Harbola

2017

Int J of Quantum Chemistry

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An accurate semianalytic wavefunction is proposed for the Hookium and two‐electron atoms for varying strength of αVee(0≤α≤1) where α is the strength parameter and Vee is coulomb interaction between two electrons. The wavefunction leads to energies that are as accurate as those from the Coupled cluster singles and doubles (CCSD) calculations. Using this wavefunction, we construct the external potential vextα such that the density of the system remains unchanged as α is varied. The work thus gives a unified picture of adiabatic connection for these systems based on an easy to use wavefunction and complements the past investigations done in this direction. Using the potential obtained, we explicitly calculate the energy of the corresponding positive ions and show that the chemical potential—calculated as the difference between the energies of the two‐electron system and its positive ion—is equal to the experimental ionization energy and remains unchanged as α is varied. Furthermore, using total energies E(α) of these systems as a function of α, we provide a new perspective into a variety of hybrid functionals.

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“…For both H

^{-}

and He atoms, its value is close to the experimental number which is

- 0.0277 au

for H

^{-}

and

- 0.9038 au

for He. For

α = 1

parameters obtained with the van Leeuwen–Barends calculations are the same as those obtained in our previous work …”

Section: Resultssupporting

confidence: 78%

“…For atoms and ions in the He isoelectronic series, the external potential is

- \frac{Z}{r}

and an accurate wavefunction for

α = 1

is given as

Ψ^{α = 1} ({\overset{r}{true}}_{1}, {\overset{r}{true}}_{2}) = ϕ ({\overset{r}{true}}_{1}) ϕ ({\overset{r}{true}}_{2}) [\cosh a r_{1} + \cosh a r_{2}]

[1 + 0.5 r_{12} e^{- b r_{12}}]

where

ϕ (\overset{r}{true})

is obtained by solving the Equation with

α = 1

and

Δ v_{ext}^{α} = 0

. The wavefunction in Equation is a generalization of the Le Sech wavefunction where

ϕ (\overset{r}{true}) = e^{- Z r}

and provides flexibility in

ϕ (\overset{r}{true})

so that the wavefunction can be varied for different values of

α

to fit a given density.…”

Section: Resultsmentioning

confidence: 99%

“…[ ] and [ ], a simple and compact semianalytic wavefunction is constructed for all values of

α

. This wavefunction is expressed as a product of orbitals and a correlation factor and is given as

Ψ^{α} ({\overset{r}{true}}_{1}, {\overset{r}{true}}_{2}) = ϕ ({\overset{r}{true}}_{1}) ϕ ({\overset{r}{true}}_{2}) f^{α} (r_{1}, r_{2}, r_{12})

where the correlation factor

f^{α} (r_{1}, r_{2}, r_{12}) = (1 + 0.5 α r_{12})

for the Hookium atom, and

f^{α} (r_{1}, r_{2}, r_{12}) = (\cosh a r_{1} + \cosh a r_{2}) (1 + 0.5 α r_{12} e^{- b r_{12}})

for atoms. In the expressions above

{\overset{r}{true}}_{1}

and

{\overset{r}{true}}_{2}

are the coordinates of the two electrons,

r_{12} = | {\overset{r}{true}}_{1} - {\overset{r}{true}}_{2} |

and

…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Study of adiabatic connection in density functional theory with an accurate wavefunction for two‐electron spherical systems

Singh

Harbola

2017

Int J of Quantum Chemistry

Self Cite

View full text Add to dashboard Cite

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“…We first perform our study using the exact densities for two-electron systems of the He atom and H − ion and the Hookium atom 42,55,56 . This enables us to analyze the functionals for two different kinds of external potentials : The external potential for H − and He atom has − 1 r dependence whereas the external potential in the Hookium atom has r 2 dependence where r is the distance from the origin.…”

Section: Resultsmentioning

confidence: 99%

“…These energies have been calculated from the near exact semi analytic densities 55,57 for H − and He and the exact density 42,56 for the Hookium atom. We note that SCAN functional has also been studied 58 for Hooke's atom recently.…”

Section: A Results For Exact Densitiesmentioning

confidence: 99%

A study of accurate exchange-correlation functionals through adiabatic connection

Singh

Harbola

2017

The Journal of Chemical Physics

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A systematic way of improving exchange-correlation energy functionals of density functional theory has been to make them satisfy more and more exact relations. Starting from the initial GGA functionals, this has culminated into the recently proposed SCAN(Strongly constrained and appropriately normed) functional that satisfies several known constraints and is appropriately normed. The ultimate test for the functionals developed is the accuracy of energy calculated by employing them. In this paper, we test these exchange-correlation functionals −the GGA hybrid functionals B3LYP and PBE0, and the meta-GGA functional SCAN− from a different perspective. We study how accurately these functionals reproduce the exchange-correlation energy when electron-electron interaction is scaled as αV ee with α varying between 0 and 1. Our study reveals interesting comparison between these functionals and the associated difference T c between the interacting and the non-interacting kinetic energy for the same density.

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Partial Separability of the Schrödinger Equation Combined with a Jastrow Factor

Le Sech,

Sarsa

2023

J. Chem. Theory Comput.

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Describing the Coulomb interactions between electrons in atomic or molecular systems is an important step to help us obtain accurate results for the different observables in the system. One convenient approach is to separate the dynamic electronic correlation, i.e., Coulomb electron–electron repulsion, from the motion of the electrons in the nucleus electric field. The wave function is written as the product of two terms, one accounting for the electron–electron interactions, which is symmetric under identical particle exchange, and the other is antisymmetric and represents the dynamics and exchange of electrons within the nuclear electric field. In this work, we present a novel computational scheme based on this idea that leads to an expression of the energy as the sum of two terms. To illustrate the method, we look into few-body Coulombic systems, H2, H3 +, and Li(1s2,2s), and discuss the possible extension to larger systems. A simple correlation factor, based on the Jastrow exponential term, is employed to represent the dynamics of the electron pairs, leading to simple analytical forms and accurate results. We also present and illustrate a different approach with the Li atom based on the partial separability applied to a portion of the atom.

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Improved Le Sech wavefunctions for two-electron atomic systems

Cited by 10 publications

References 28 publications

Study of adiabatic connection in density functional theory with an accurate wavefunction for two‐electron spherical systems

Study of adiabatic connection in density functional theory with an accurate wavefunction for two‐electron spherical systems

A study of accurate exchange-correlation functionals through adiabatic connection

Partial Separability of the Schrödinger Equation Combined with a Jastrow Factor

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