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An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
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Electrons are negatively charged subatomic particles attracted to and orbit around the positively-charged nucleus of an atom. They reside in spaces associated with energy levels called shells and are further organized into subshells and orbitals within each shell.
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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
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Dalton was only partially correct about the particles that make up matter. All matter is composed of atoms, and atoms are composed of three smaller subatomic particles: protons, neutrons, and electrons. These three particles account for the mass and the charge of an atom.
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Area of Science:

  • Quantum chemistry
  • Computational physics

Background:

  • Electronic structure calculations are fundamental to understanding molecular behavior.
  • Density functional theory (DFT) is a widely used approximation for electronic structure.
  • Limitations exist in current DFT approximations, particularly for systems with strong electron correlation or fractional particle numbers.

Purpose of the Study:

  • To demonstrate discontinuous changes in electronic structure with infinitesimal Hamiltonian changes.
  • To investigate electron behavior in one and two electron molecular systems using fractional nuclear charges.
  • To highlight the shortcomings of current DFT methods in capturing these phenomena.

Main Methods:

  • Full configuration interaction (FCI) calculations were employed.
  • The nuclear charge was extended to be fractional.
  • Analysis of electron densities in real space was performed.

Main Results:

  • Discontinuous changes in electronic structure were observed upon infinitesimal Hamiltonian changes.
  • FCI electron densities showed dramatic real-space changes, including electron transfer, hopping, and removal.
  • Significant errors in DFT-predicted electron densities were identified when compared to FCI results.

Conclusions:

  • The particle nature of electrons and energy derivative discontinuities are crucial for accurately describing molecular systems.
  • Current DFT approximations fail to capture essential physics, leading to dramatic errors in electron densities.
  • Accurate modeling of electron movement, vital for chemical reactions and electron transport, presents a significant challenge for developing new electronic structure methods.