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Related Concept Videos

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,...
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...
Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
Valence Bond Theory and Hybridized Orbitals02:38

Valence Bond Theory and Hybridized Orbitals

According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...
Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...

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Updated: May 16, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Published on: April 8, 2020

DFTB3: Extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB).

Michael Gaus, Qiang Cui, Marcus Elstner

    Journal of Chemical Theory and Computation
    |December 4, 2012
    PubMed
    Summary

    The new DFTB3 method improves calculations for charged biomolecular systems by incorporating third-order energy expansion and better Coulomb interactions. This enhances accuracy for hydrogen binding energies and proton affinities.

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    Published on: August 22, 2017

    Area of Science:

    • Computational chemistry
    • Quantum chemistry
    • Materials science

    Background:

    • The self-consistent-charge density-functional tight-binding (SCC-DFTB) method is an approximation of density functional theory (DFT).
    • SCC-DFTB is based on a second-order expansion of the DFT total energy.
    • Existing SCC-DFTB methods have limitations in describing charged systems.

    Purpose of the Study:

    • To develop an improved DFTB methodology, termed DFTB3.
    • To enhance the description of charged systems, particularly those relevant to biomolecules.
    • To improve the accuracy of calculated hydrogen binding energies and proton affinities.

    Main Methods:

    • Combined earlier extensions of SCC-DFTB.
    • Incorporated an improved Coulomb interaction model for atomic partial charges.
    • Included the complete third-order expansion of the DFT total energy.

    Main Results:

    • The DFTB3 method shows substantial improvements in describing charged systems.
    • Accuracy is significantly enhanced for elements C, H, N, O, and P.
    • Hydrogen binding energies and proton affinities are more accurately predicted.

    Conclusions:

    • DFTB3 represents a significant advancement in DFTB methodology.
    • The method is particularly well-suited for biomolecular simulations.
    • Further research directions and potential solutions for remaining challenges are discussed.