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Related Concept Videos

Atomic Radii and Effective Nuclear Charge03:08

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number and distribution of electrons in their valence shells.
Thermodynamic Potentials01:26

Thermodynamic Potentials

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

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.
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

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. Schrödinger...
Electron Configurations02:46

Electron Configurations

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, 4s,...
Electronic Structure of Atoms02:28

Electronic Structure of Atoms


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 numbers:  n, l, ml, and...

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Updated: Jul 8, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Published on: May 27, 2020

Energy-consistent relativistic pseudopotentials for the 4d elements: atomic and molecular applications.

Detlev Figgen1, Kirk A Peterson, Hermann Stoll

  • 1Centre of Theoretical Chemistry and Physics, Institute of Fundamental Sciences, Massey University, Auckland, New Zealand.

The Journal of Chemical Physics
|January 22, 2008
PubMed
Summary

This study precisely calculated atomic and molecular properties for 4d metals using advanced computational methods. Results show excellent agreement with experimental data, refining understanding of electronic structures and properties.

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Last Updated: Jul 8, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Atomic and Molecular Science

Background:

  • Accurate calculation of atomic and molecular properties is crucial for understanding chemical behavior.
  • Relativistic effects and electron correlation significantly influence properties of heavy elements.

Purpose of the Study:

  • To benchmark energy-consistent relativistic pseudopotentials and correlation consistent basis sets for 4d metals.
  • To investigate electron affinities, excitation energies, and ionization potentials of 4d metals.
  • To compute electronic states of ZrO, RuF, and Pd2 molecules.

Main Methods:

  • Coupled cluster calculations up to CCSDTQ level.
  • Douglas-Kroll-Hess (DKH) all-electron calculations.
  • Pseudopotential calculations with spin-orbit coupling.
  • Systematic sequences of correlation consistent basis sets.

Main Results:

  • Calculated atomic properties are within 1 kcal/mol of experimental values.
  • Suggested a revised experimental value for the ionization potential of Technetium (Tc).
  • Accurately predicted molecular electronic states, including the ground state of RuF.

Conclusions:

  • The employed computational methods provide highly accurate predictions for atomic and molecular properties.
  • Validated the use of energy-consistent pseudopotentials and basis sets for heavy elements.
  • Demonstrated the importance of including relativistic effects and electron correlation for precise calculations.