Orbital-free quantum crystallography: view on forces in crystals
Vladimir Tsirelson1, Adam Stash2
1Quantum Chemistry Department, D.I. Mendeleev University of Chemical Technology, Miusskaya Square, 9, Moscow, 125047, Russian Federation.
Summary
This study combines quantum theory of atoms in molecules and orbital-free density functional theory to analyze forces in crystals. It reveals how kinetic and potential forces balance, influencing electron distribution and forming atomic shells.
Area of Science:
- Solid-state physics and quantum chemistry.
- Investigates electronic structure and forces within crystalline materials.
Background:
- Understanding electron distribution is crucial for predicting material properties.
- Traditional methods often rely on atomic orbitals, limiting applicability.
Purpose of the Study:
- To combine quantum theory of atoms in molecules (QTAIM) with orbital-free density functional theory (DFT).
- To study the spatial distribution of electrostatic and quantum electronic forces in stable crystals.
- To develop an orbital-free quantum crystallography approach.
Main Methods:
- Utilized QTAIM and orbital-free DFT to analyze electron distribution and forces.
- Expressed forces in terms of kinetic and DFT potentials derived from experimental electron density.
- Analyzed critical points of kinetic and potential fields, identifying Lagrange points.
Main Results:
- Identified a balance between kinetic (Fkin(r)) and potential (F(r)) forces at equilibrium.
- Found that potential forces attract electrons to nuclei, while kinetic forces draw them away.
- Observed that only kinetic potential exhibits electronic shells and atomic-like basins around nuclei.
Conclusions:
- The developed orbital-free approach provides insights into electron distribution and forces in crystals.
- The interplay between kinetic and potential forces dictates electron localization and bonding.
- Distinctions between force-field approaches and QTAIM are clarified.
Related Concept Videos
02:58Crystal Field Theory - Octahedral Complexes
29.6K
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...
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...
29.6K
02:46Crystal Field Theory - Tetrahedral and Square Planar Complexes
46.9K
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,...
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,...
46.9K
02:18X-ray Crystallography
25.4K
The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
25.4K
03:00Intermolecular vs Intramolecular Forces
94.7K
Intermolecular forces (IMF) are electrostatic attractions arising from charge-charge interactions between molecules. The strength of the intermolecular force is influenced by the distance of separation between molecules. The forces significantly affect the interactions in solids and liquids, where the molecules are close together. In gases, IMFs become important only under high-pressure conditions (due to the proximity of gas molecules). Intermolecular forces dictate the physical properties of...
94.7K
02:35Molecular Orbital Theory I
44.8K
Overview of Molecular Orbital Theory
44.8K
02:40MO Theory and Covalent Bonding
13.2K
The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
13.2K