Complete and Orthonormal Sets of Exponential-type Orbitals with non-integer quantum numbers. On the results for many-electron atoms using Roothaan's LCAO method

• URL: http://arxiv.org/abs/2507.04305v1
• Date: Sun, 06 Jul 2025 09:15:11 GMT
• Title: Complete and Orthonormal Sets of Exponential-type Orbitals with non-integer quantum numbers. On the results for many-electron atoms using Roothaan's LCAO method
• Authors: Ali Bagci, Philip E. Hoggan,
• Abstract summary: A method is proposed to construct accurate and computationally efficient basis sets using these orbitals.<n>Results are lower than those reported using other published basis sets.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Complete orthonormal sets of exponential-type orbitals with non-integer principal quantum numbers are discussed as basis functions in non-relativistic Hartree-Fock-Roothaan electronic structure calculations of atoms. A method is proposed to construct accurate and computationally efficient basis sets using these orbitals. It is demonstrated that principal quantum numbers of fractional order cannot be treated solely as variational parameters, since such a procedure may lead to unphysical basis sets (in particular, linearly dependent Slater-type functions). Ground-state total energies for the Be- and Ne- isoelectronic series are calculated. The results obtained are lower than those reported using other published basis sets. However, the energies obtained using Slater-type functions with non-integer principal quantum numbers are omitted from the comparison. These "orbitals" have no physical interpretation (except the "1s", which coincides with a hydrogenlike eigenfunction). In general linear independence of such Slater-type orbitals is not guaranteed. The results confirm that the parameter alpha, used to represent the complete orthonormal exponential-type orbitals in the weighted Hilbert space, is neither observable nor suitable to be considered as a variational parameter, despite its treatment as such in some prior work.

Related papers

• Approximating Hamiltonian for Hartree-Fock solutions for nonrelativistic atoms [0.0]
  We compute the binding energy, ionization potentials, electron density distribution, electron density at the nucleus, and atomic scattering factors of nonrelativistic atoms and ions.<n>The accuracy of our results is comparable with those obtained via the usage of the Hartree-Fock method.
  arXiv  Detail & Related papers  (2025-06-17T15:52:41Z)
• New Atomic Orbital Functions.Complete and Orthonormal Sets of ETOs with Non-integer Quantum Numbers.Results for He-like atoms [0.0]
  Hartree-Fock-Rothaan equations for He-like ions are solved using the iterative self-consistent method.<n>New complete and orthonormal sets of exponential-type orbitals are employed as the basis.
  arXiv  Detail & Related papers  (2025-04-14T10:42:04Z)
• Efficient conversion from fermionic Gaussian states to matrix product states [48.225436651971805]
  We propose a highly efficient algorithm that converts fermionic Gaussian states to matrix product states.<n>It can be formulated for finite-size systems without translation invariance, but becomes particularly appealing when applied to infinite systems.<n>The potential of our method is demonstrated by numerical calculations in two chiral spin liquids.
  arXiv  Detail & Related papers  (2024-08-02T10:15:26Z)
• Neural Pfaffians: Solving Many Many-Electron Schrödinger Equations [58.130170155147205]
  Neural wave functions accomplished unprecedented accuracies in approximating the ground state of many-electron systems, though at a high computational cost. Recent works proposed amortizing the cost by learning generalized wave functions across different structures and compounds instead of solving each problem independently. This work tackles the problem by defining overparametrized, fully learnable neural wave functions suitable for generalization across molecules.
  arXiv  Detail & Related papers  (2024-05-23T16:30:51Z)
• A Theory of Quantum Jumps [44.99833362998488]
  We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
  arXiv  Detail & Related papers  (2024-04-16T11:00:46Z)
• Natural orbitals and sparsity of quantum mutual information [0.0]
  We show that the converged orbitals are coinciding with natural orbitals. The correlation is encoded in a smaller number of qubit pairs contributing to the quantum mutual information matrix.
  arXiv  Detail & Related papers  (2023-08-15T21:51:53Z)
• Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
  Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
  arXiv  Detail & Related papers  (2022-10-19T02:28:44Z)
• Natural orbitals for the ab initio no-core configuration interaction approach [0.13999481573773068]
  We seek to improve the accuracy obtained for a given basis size by optimizing the choice of single-particle orbitals. Natural orbitals, which diagonalize the one-body density matrix, provide a basis which maximizes the occupation of low-lying orbitals. We explore aspects of NCCI calculations with natural orbitals for the ground state of the $p$-shell neutron halo nucleus.
  arXiv  Detail & Related papers  (2021-12-07T22:38:39Z)
• A Quantum Mechanical Justification of Bohr Atomic Model [0.0]
  Bohr atomic model is based on the assumption that electrons on allowed quantized orbits do not radiate. Main results include the values of the radii of circular quantized orbits and of the hydrogen atom energy levels.
  arXiv  Detail & Related papers  (2021-05-06T15:49:56Z)
• Quantum deleting and cloning in a pseudo-unitary system [20.489044283783358]
  We investigate the quantum deleting and cloning in a pseudo-unitary system. We show that it is possible to delete and clone a class of two different and nonorthogonal states. We simulate the pseudo-unitary operators in conventional quantum mechanics with post-selection.
  arXiv  Detail & Related papers  (2021-03-29T05:59:27Z)
• A multiconfigurational study of the negatively charged nitrogen-vacancy center in diamond [55.58269472099399]
  Deep defects in wide band gap semiconductors have emerged as leading qubit candidates for realizing quantum sensing and information applications. Here we show that unlike single-particle treatments, the multiconfigurational quantum chemistry methods, traditionally reserved for atoms/molecules, accurately describe the many-body characteristics of the electronic states of these defect centers.
  arXiv  Detail & Related papers  (2020-08-24T01:49:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.