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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...
Atomic Spectroscopy: Effects of Temperature01:27

Atomic Spectroscopy: Effects of Temperature

Atomization, converting samples into gas-phase atoms and ions, is essential for atomic spectroscopy. The flame temperature required for atomization affects the efficiency of the atomic spectroscopic methods by increasing the atomization efficiency and the relative population of the excited and ground states.
At thermal equilibrium, the relative populations of excited and ground state atoms can be estimated using the Maxwell–Boltzmann distribution. For example, an increase in temperature from...
Properties of Transition Metals02:58

Properties of Transition Metals

Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3–12 are transition elements. The f-block elements, also called inner transition metals (the lanthanides and actinides), also meet this criterion because the d orbital is partially occupied before the f orbitals.
Bonding in Metals02:32

Bonding in Metals

Metallic bonds are formed between two metal atoms. A simplified model to describe metallic bonding has been developed by Paul Drüde called the “Electron Sea Model”.
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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: May 24, 2026

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

Quantum-mechanical interatomic potentials with electron temperature for strong-coupling transition metals.

John A Moriarty1, Randolph Q Hood, Lin H Yang

  • 1Condensed Matter and Materials Division, Lawrence Livermore National Laboratory, Livermore, California 94551-0808, USA. moriarty2@llnl.gov

Physical Review Letters
|March 10, 2012
PubMed
Summary
This summary is machine-generated.

Electron temperature significantly influences the electronic structure and interatomic forces in transition metals near melting. New potentials accurately model molybdenum

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Computational Materials Science

Background:

  • Electron temperature (T(el)) critically affects electronic structure in narrow d-band transition metals at elevated temperatures.
  • This coupling links ion and electron thermal energy, influencing interatomic forces and material behavior near the melting point.

Purpose of the Study:

  • To develop T(el)-dependent interatomic potentials for transition metals.
  • To accurately model the high-pressure melting curve and phase diagram of molybdenum (Mo).

Main Methods:

  • Extended first-principles generalized pseudopotential theory (GPT) to finite electron temperatures, based on the Mermin formulation of density functional theory.
  • Developed efficient T(el)-dependent model GPT interatomic potentials for Mo.
  • Validated against density functional theory (DFT) quantum simulations and dynamic experimental data.

Main Results:

  • The T(el)-dependent GPT potentials accurately predict the high-pressure melting curve of Mo.
  • Results align with DFT simulations and experimental findings.
  • The potentials reveal a complex high-temperature and high-pressure polymorphism in Mo.

Conclusions:

  • Electron temperature is crucial for accurate modeling of transition metal behavior under extreme conditions.
  • The developed T(el)-dependent potentials provide a powerful tool for materials simulations.
  • This approach enables exploration of high-pressure, high-temperature phase diagrams and material properties.