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Related Concept Videos

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,...
Atomic Orbitals02:44

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
The Aufbau Principle and Hund's Rule03:02

The Aufbau Principle and Hund's Rule

To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the subshell of...
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...
Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Efficient sampling of atomic configurational spaces.

Lívia B Pártay1, Albert P Bartók, Gábor Csányi

  • 1University Chemical Laboratory, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom. lb415@cam.ac.uk

The Journal of Physical Chemistry. B
|August 13, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a novel nested sampling method for efficiently exploring chemical system energy landscapes. This approach enables unbiased potential energy surface analysis and accurate free energy calculations for atomic systems.

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Area of Science:

  • Computational Chemistry
  • Statistical Mechanics
  • Chemical Physics

Background:

  • Exploring the configurational phase space of chemical systems is crucial for understanding their behavior.
  • Existing methods may face limitations in efficiency and unbiased exploration of potential energy surfaces (PES).

Purpose of the Study:

  • To present a new method based on the nested sampling algorithm for efficient and unbiased exploration of chemical system phase space.
  • To demonstrate the application of this method to Lennard-Jones (LJ) clusters and determine their temperature-density phase diagram.

Main Methods:

  • Utilizing the nested sampling algorithm to explore the entire potential energy surface (PES).
  • Employing two parameters to control the trade-off between exploration resolution and computational cost.
  • Calculating partition functions and expectation values as a postprocessing step.

Main Results:

  • Demonstrated efficient and unbiased exploration of the PES for LJ clusters.
  • Enabled determination of the temperature-density phase diagram for LJ cluster stability through absolute free energy calculations.
  • Achieved significant efficiency gains (order of magnitude or more) over parallel tempering for heat capacity calculations.
  • Identified an order parameter to define macroscopic states and evaluate free energies by analyzing PES topology.

Conclusions:

  • The nested sampling method provides an efficient and unbiased approach to explore chemical configurational phase space.
  • This method facilitates the calculation of absolute free energies, enabling the construction of phase diagrams.
  • The approach offers a novel way to visualize PES and unambiguously define macroscopic states of atomistic systems.