Browsing by Author "Rabeet Singh"

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A new variational wave-function ansatz for confined two-electron atomic systems
(Institute of Physics, 2025) Deepak Singh; Rabeet Singh; Arup Banerjee
In this paper, we propose a simple variational ansatz, Ψ(r⃗1,r⃗2) = C sin (π rc r1) sin( π rc r2) exp(−Z(r1 + r2))[cosh(ar1) + cosh(ar2)][1 + 0.5r12 exp(−br12)], r1 r2 to study confined two-electron atomic systems. Here, r12 = |r-1 −-2| is the inter-electronic distance with the electron coordinatesr-1 andr-2, rc is the radius of the impenetrable well in which the two-electron atoms are confined, and C is the normalization constant. The function sin(πr/rc)/r incorporates the Dirichlet boundary conditions at r = rc needed for the wave function of two-electron systems, and a and b are the variational parameters evaluated by minimizing the total energy functional of confined two-electron atoms. We also calculate the pressure and check the satisfaction of the virial relation for such systems. Our results for the ground-state energy and its components, radial distance moments, and pressure show agreement with the existing literature. © 2025 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.
Calculation of electronic and response properties of a hydrogen atom in soft confinement potential: a variational approach
(Institute of Physics, 2025) Dakshata Mandloi; Rabeet Singh; Arup Banerjee
The electronic properties of atoms confined in finite or infinite boxes with discontinuity have been extensively studied by the researchers. Recently, smooth or continuous versions of such confining potentials given by V conf ( r ) = ( r R ) N with stiffness parameter N and confinement radius R have been considered. This soft-potential coincides with the infinite discontinuous hard-wall potential as N ⟶ ∞ . In this paper, we study the electronic properties of a hydrogen atom confined in a soft-wall potential using a variational approach. For this purpose, we construct the variational wave functions representing the ground state as well as a few low-lying excited states. The variational wave functions yield quite accurate results for a wide range of values of R and N. We also employ the variational ground-state wave function to calculate dipole (α1) and quadrupole (α2) polarizabilities and van der Waals coefficients C6 and C8 © 2025 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.
Erratum: Semianalytical wavefunctions and Kohn-Sham exchange-correlation potentials for two-electron atomic systems in two-dimensions (Journal of Physics B: Atomic, Molecular and Optical Physics (2020) 53 (035001) DOI: 10.1088/1361-6455/ab56be)
(IOP Publishing Ltd, 2021) Rabeet Singh; Ashish Kumar; Manoj K. Harbola; Prasanjit Samal
Recently, we proposed accurate forms of the wavefunction for two-electron atomic systems in two-dimensions and calculated the exchange–correlation potentials for these systems using the Levy–Perdew–Sahni (LPS) equation. As a part of this work, we reported the results for the chemical potentials (μ) calculated by solving the LPS equation (Formula Presented) directly. For this, we construct the effective potential vLPS eff (ir ) for Le Sech and modified Le Sech wavefunction, and then solve the LPS equation to get the chemical potential and density (?). The values so obtained for μ for the modified Le Sech wavefunctions given in table 7 of this paper are not correct. In this erratum, we correct these and give table 7 of the paper mentioned above with updated values of μ for the modified Le Sech wavefunctions (Table Presented). © 2021 Institute of Physics Publishing. All rights reserved.
Levy-Perdew-Sahni equation and its application to perform atomic calculations
(American Institute of Physics, 2025) Rabeet Singh; Ashish Kumar; Manoj Kumar Harbola
Levy-Perdew-Sahni (LPS) derived the connection between the asymptotic decay of density and the ionization potential of a many-electron system using the equation for the square root of density. For this, they employed an expression for the corresponding effective potential in terms of the wavefunction of the system. In this paper, we explore the possibility of solving the LPS equation in conjunction with approximate wavefunction. For this, we first perform the variational derivation of the equation and use this to set up a self-consistent cycle to get the ground state properties of two-electron systems using the modified form of the Le Sech wavefunction. Furthermore, using the observation that even the approximate wavefunctions give the accurate effective potential for the LPS equation, we show that accurate densities are obtained through using the LPS equation with these wavefunctions. We demonstrate our method by performing calculations for closed-shell atoms. © 2025 Author(s).
Modified Le Sech wavefunction for investigating confined two-electron atomic systems
(Springer Science and Business Media Deutschland GmbH, 2024) Rabeet Singh; Arup Banerjee
Abstract: In this article, we propose an alternate approach to study confined two-electron systems using the modified form of the Le Sech wavefunction. In the present approach, rather than using the cut-off factor in the variational wavefunction, we determine it directly by solving Schrödinger like equation. The results for kinetic energies, electron-nucleus interaction, electron–electron interaction, total energies, densities, ionization energies, and moments of confined H- and He atom are compared with the most accurate values found in the literature to show the effectiveness of our method. The present approach applies to a wide range of confinement potentials. We demonstrate it by showing the results for Coulomb, harmonic oscillator, and soft-confinement potentials. Graphic abstract: (Figure presented.). © The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024.