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Related Concept Videos

Electron Configurations02:46

Electron Configurations

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Electron configurations and orbital diagrams can be determined by applying the Aufbau principle (each added electron occupies the subshell of lowest energy available), Pauli exclusion principle (no two electrons can have the same set of four quantum numbers), and Hund’s rule of maximum multiplicity (whenever possible, electrons retain unpaired spins in degenerate orbitals).
The relative energies of the subshells determine the order in which atomic orbitals are filled (1s, 2s, 2p, 3s, 3p,...
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The Energies of Atomic Orbitals03:21

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In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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Molecular Orbital Theory II

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Molecular Orbital Energy Diagrams
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Electronic Structure of Atoms02:28

Electronic Structure of Atoms

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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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The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Updated: Oct 17, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Multi-Basis-Set (TD-)DFT Methods for Predicting Electron Attachment Energies.

Guillaume Thiam1, Franck Rabilloud1

  • 1Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, UMR5306, F-69622 Villeurbanne, France.

The Journal of Physical Chemistry Letters
|October 7, 2021
PubMed
Summary
This summary is machine-generated.

Calculating temporary anion resonance energies is challenging. This study introduces a reliable computational method using ab initio (time-dependent) density functional theory (TD-DFT) to accurately predict these energies for electron-molecule interactions.

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Area of Science:

  • Physical Chemistry
  • Computational Chemistry
  • Quantum Chemistry

Background:

  • Low-energy electron collisions with molecules can form temporary anions through resonant processes.
  • Experimental techniques like electron transmission spectroscopy are effective but simulating electron attachment remains difficult.

Purpose of the Study:

  • To develop and validate a computational methodology for calculating electron attachment resonance energies.
  • To provide a reliable theoretical approach for studying temporary anions.

Main Methods:

  • Utilizing ab initio (time-dependent) density functional theory (TD-DFT) calculations.
  • Employing two distinct basis sets: a large one with diffuse functions for vertical electron affinity and a smaller one for anion excitation energy.
  • Calculating 53 resonance energies for 18 different molecules.

Main Results:

  • The proposed computational method demonstrates high reliability in predicting resonance energies.
  • Calculated values show good agreement with existing experimental data.

Conclusions:

  • The developed TD-DFT methodology offers an accurate and efficient approach for simulating electron attachment processes.
  • This method can aid in the characterization of temporary anions in molecular systems.