Related Experiment Video
Updated: May 16, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Anharmonic motion in experimental charge density investigations
Regine Herbst-Irmer1, Julian Henn, Julian J Holstein
1Institut für Anorganische Chemie, Universität Göttingen, Tammannstrasse 4, 37077 Göttingen, Germany. rherbst@shelx.uni-ac.gwdg.de
The Journal of Physical Chemistry. A
|December 18, 2012
Summary
Anharmonic motion in crystals, even at low temperatures, requires advanced models like Gram-Charlier coefficients. This study proves anharmonic models are superior to disorder models for accurate charge density analysis.
Area of Science:
- Crystallography
- Solid-state chemistry
- Computational chemistry
Background:
- Accurate charge density analysis is crucial for understanding chemical bonding and electronic structure.
- Thermal motion of atoms can complicate crystallographic refinements, potentially leading to inaccurate models.
- Distinguishing between anharmonic motion and positional disorder is a persistent challenge in crystallography.
Purpose of the Study:
- To investigate the necessity and superiority of anharmonic models over disorder models in charge density studies.
- To analyze the impact of unrefined anharmonic motion on crystallographic parameters and residual density.
- To establish reliable methods for detecting and refining anharmonic atomic motion.
Main Methods:
- Charge density refinement of 9-diphenylthiophosphinoylanthracene using multiple temperature datasets.
- Application of the Gram-Charlier expansion for describing anharmonic atomic motion.
- Comparison of anharmonic models with conventional disorder models.
- Analysis of residual electron density patterns and probability density functions.
Main Results:
- Anharmonic motion was necessary for several atoms even at 15 K, indicating its significance at low temperatures.
- The anharmonic model demonstrated superiority over the disorder model, especially when atomic displacements were larger.
- Unrefined anharmonic motion resulted in distorted multipole parameters and characteristic 'shashlik-like' residual density patterns.
- Gram-Charlier coefficients provided a more accurate description of atomic motion compared to disorder models.
Conclusions:
- Properly detecting and refining anharmonic motion is essential for accurate charge density analysis.
- Anharmonic models offer a more physically realistic description of atomic thermal motion than disorder models in certain cases.
- Analysis of residual density and probability density functions are key indicators for identifying anharmonicity.
More Related Videos
Related Concept Videos
01:22Motion Of A Charged Particle In A Magnetic Field
A charged particle experiences a force when moving through a magnetic field. Consider the field to be uniform and the charged particle to move perpendicular to it. If the field is in a vacuum, the magnetic field is the dominant factor determining the motion. Since the magnetic force is perpendicular to the direction of motion, a charged particle follows a curved path. The particle continues to follow this curved path until it forms a complete circle. Another way to look at this is that the...
01:17Continuous Charge Distributions
Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
The electric charge can also be subjected to an analogical...
01:23Magnetic Field due to Moving Charges
A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...
01:17Characteristics of Simple Harmonic Motion
The key characteristic of the simple harmonic motion is that the acceleration of the system and, therefore, the net force are proportional to the displacement and act in the opposite direction to the displacement. Additionally, the period and frequency of a simple harmonic oscillator are independent of its amplitude. For example, diving boards move faster or slower based on their thickness. A stiff, thick diving board has a large force constant, which causes it to have a smaller period, while a...
01:30The Hall Effect
Edwin H. Hall, in the year 1879, devised an experiment that could be used to identify the polarity of the predominant charge carriers in a conducting material. From a historical perspective, this experiment was the first to demonstrate that the charge carriers in most metals are negative.
01:24Electrochemical Systems
Electrochemical systems provide a fascinating insight into the dynamic interplay of charged species within various phases. One notable example is the interaction between a membrane permeable to K⁺ ions but not to Cl⁻ ions, separating an aqueous KCl solution from pure water. As K⁺ ions diffuse through the membrane, they generate net charges on each phase, leading to a potential difference between them.Similarly, when a piece of Zn is immersed in an aqueous ZnSO₄ solution, the Zn metal, composed...