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Related Concept Videos

Structures of Solids02:22

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Resonance and Hybrid Structures02:16

Resonance and Hybrid Structures

According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
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...
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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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Solid-solid structural transformations in Lennard-Jones clusters: accurate simulations versus the harmonic

Vladimir A Sharapov1, Vladimir A Mandelshtam

  • 1Chemistry Department, University of California at Irvine, Irvine, California 92697, USA.

The Journal of Physical Chemistry. A
|August 10, 2007
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This study introduces a novel Monte Carlo (MC) method to efficiently overcome broken ergodicity in low-temperature solid-solid transitions. The new approach accurately samples systems with high energy barriers, validating existing approximations.

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Area of Science:

  • Computational Chemistry
  • Statistical Mechanics
  • Materials Science

Background:

  • Low-temperature solid-solid transitions present challenges due to high potential barriers and similar energy minima.
  • The broken-ergodicity problem hinders accurate simulations, even with advanced methods like Replica Exchange Monte Carlo (REM).

Purpose of the Study:

  • To develop a numerically accurate and efficient methodology for simulating systems with broken ergodicity.
  • To improve sampling efficiency in low-temperature phase transitions.

Main Methods:

  • Implementation of a new Monte Carlo (MC) move within the Replica Exchange Method (REM) framework.
  • Analytical generation of trial points using an auxiliary harmonic superposition system mimicking the true system at low temperatures.

Main Results:

  • The new MC move enables frequent switching between potential energy funnels, leading to efficient sampling.
  • Accurate results were obtained for Lennard-Jones clusters, validating the Harmonic Superposition Approximation (HSA).

Conclusions:

  • The developed methodology effectively addresses broken ergodicity in complex systems.
  • The study validates the reliability of the Harmonic Superposition Approximation (HSA) for estimating low-temperature solid-solid transition temperatures.