Ground State Energies of Helium-Like Ions Using a Simple Parameter-Free Matrix Method
This study aims to use hydrogenic orbitals within an analytic and numeric parameter-free truncated-matrix method to solve the projected Schrödinger equation of some Helium-like ions (3 ≤ Z ≤ 10). We also derived a new analytical expression of the ion ground state energies, which was simple and accur...
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Department of Chemistry, Universitas Gadjah Mada
2021
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oai:doaj.org-article:b7d8044667544bab8904b558d3d1d5d32021-12-02T18:41:46ZGround State Energies of Helium-Like Ions Using a Simple Parameter-Free Matrix Method1411-94202460-157810.22146/ijc.65737https://doaj.org/article/b7d8044667544bab8904b558d3d1d5d32021-07-01T00:00:00Zhttps://jurnal.ugm.ac.id/ijc/article/view/65737https://doaj.org/toc/1411-9420https://doaj.org/toc/2460-1578This study aims to use hydrogenic orbitals within an analytic and numeric parameter-free truncated-matrix method to solve the projected Schrödinger equation of some Helium-like ions (3 ≤ Z ≤ 10). We also derived a new analytical expression of the ion ground state energies, which was simple and accurate and improved the accuracy of the analytic calculation, numerically using Mathematica. The standard matrix method was applied, where the wave function of the ions was expanded in a finite number of eigenvectors comprising hydrogenic orbitals. The Hamiltonian of the systems was calculated using the wave function and diagonalized to obtain their ground state energies. The results showed that a simple analytic expression of the ground state energies of He-like ions was successfully derived. Although the analytic expression was derived without involving any variational parameter, it was reasonably accurate with a 0.12% error for Ne8+ ion. From this method, the accuracy of the analytic energies was also numerically improved to 0.10% error for Ne8+ ion. The results clearly showed that the energies obtained using this method were more accurate than the hydrogenic perturbation theory and the uncertainty principle-variational approach. In addition, for Z > 4, our results were more accurate than those from the geometrical model.Redi Kristian PingakAtika AhabUtama Alan DetaDepartment of Chemistry, Universitas Gadjah Madaarticlehelium-like ionsground state energiesparameter-free matrix methodhydrogenic orbital approximationprojected schrödinger equationChemistryQD1-999ENIndonesian Journal of Chemistry, Vol 21, Iss 4, Pp 1003-1015 (2021) |
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helium-like ions ground state energies parameter-free matrix method hydrogenic orbital approximation projected schrödinger equation Chemistry QD1-999 |
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helium-like ions ground state energies parameter-free matrix method hydrogenic orbital approximation projected schrödinger equation Chemistry QD1-999 Redi Kristian Pingak Atika Ahab Utama Alan Deta Ground State Energies of Helium-Like Ions Using a Simple Parameter-Free Matrix Method |
| description |
This study aims to use hydrogenic orbitals within an analytic and numeric parameter-free truncated-matrix method to solve the projected Schrödinger equation of some Helium-like ions (3 ≤ Z ≤ 10). We also derived a new analytical expression of the ion ground state energies, which was simple and accurate and improved the accuracy of the analytic calculation, numerically using Mathematica. The standard matrix method was applied, where the wave function of the ions was expanded in a finite number of eigenvectors comprising hydrogenic orbitals. The Hamiltonian of the systems was calculated using the wave function and diagonalized to obtain their ground state energies. The results showed that a simple analytic expression of the ground state energies of He-like ions was successfully derived. Although the analytic expression was derived without involving any variational parameter, it was reasonably accurate with a 0.12% error for Ne8+ ion. From this method, the accuracy of the analytic energies was also numerically improved to 0.10% error for Ne8+ ion. The results clearly showed that the energies obtained using this method were more accurate than the hydrogenic perturbation theory and the uncertainty principle-variational approach. In addition, for Z > 4, our results were more accurate than those from the geometrical model. |
| format |
article |
| author |
Redi Kristian Pingak Atika Ahab Utama Alan Deta |
| author_facet |
Redi Kristian Pingak Atika Ahab Utama Alan Deta |
| author_sort |
Redi Kristian Pingak |
| title |
Ground State Energies of Helium-Like Ions Using a Simple Parameter-Free Matrix Method |
| title_short |
Ground State Energies of Helium-Like Ions Using a Simple Parameter-Free Matrix Method |
| title_full |
Ground State Energies of Helium-Like Ions Using a Simple Parameter-Free Matrix Method |
| title_fullStr |
Ground State Energies of Helium-Like Ions Using a Simple Parameter-Free Matrix Method |
| title_full_unstemmed |
Ground State Energies of Helium-Like Ions Using a Simple Parameter-Free Matrix Method |
| title_sort |
ground state energies of helium-like ions using a simple parameter-free matrix method |
| publisher |
Department of Chemistry, Universitas Gadjah Mada |
| publishDate |
2021 |
| url |
https://doaj.org/article/b7d8044667544bab8904b558d3d1d5d3 |
| work_keys_str_mv |
AT redikristianpingak groundstateenergiesofheliumlikeionsusingasimpleparameterfreematrixmethod AT atikaahab groundstateenergiesofheliumlikeionsusingasimpleparameterfreematrixmethod AT utamaalandeta groundstateenergiesofheliumlikeionsusingasimpleparameterfreematrixmethod |
| _version_ |
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