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Resonance and Hybrid Structures

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.

MO Theory and Covalent Bonding

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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...

Molecular Orbital Theory I

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Molecular Orbital Theory II

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Structure of Benzene: Molecular Orbital Model

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According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).

Valence Bond Theory and Hybridized Orbitals

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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...

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Ensemble Force Spectroscopy by Shear Forces

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Bandstructure meets many-body theory: the LDA+DMFT method.

K Held¹, O K Andersen, M Feldbacher

¹Max-Planck Institut für Festkörperforschung, D-70569 Stuttgart, Germany.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|June 23, 2011

Summary

This summary is machine-generated.

A new method combining Density-Functional Theory (DFT) and Dynamical Mean-Field Theory (DMFT) accurately models materials with strong electronic correlations. This approach, LDA+DMFT, is crucial for understanding complex materials like LaMnO(3) and their properties.

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Area of Science:

Solid-state theory
Computational materials science
Condensed matter physics

Background:

Accurate ab initio calculation of electronic properties is challenging for strongly correlated electron systems.
Traditional Density-Functional Theory (DFT), like Local Density Approximation (LDA), is insufficient for materials with strong electronic correlations (d- or f-electrons).
Strongly correlated materials exhibit significant responses to external parameters, making them vital for technological applications.

Purpose of the Study:

To introduce and validate the combined LDA+DMFT method for ab initio calculations of strongly correlated materials.
To demonstrate the capability of LDA+DMFT in describing materials with varying degrees of electronic correlation.
To present results for LaMnO(3) and discuss its relevance to colossal magnetoresistance in doped manganites.

Main Methods:

Development and application of a hybrid approach combining DFT (specifically LDA) with Dynamical Mean-Field Theory (DMFT).
Utilizing LDA+DMFT to perform ab initio calculations for materials with strongly correlated electrons.
Case study using LaMnO(3) to illustrate the method's performance and predictive power.

Main Results:

The LDA+DMFT method successfully predicts different electronic states (weakly correlated metal, strongly correlated metal, Mott insulator) based on increasing Coulomb correlations.
Calculations for LaMnO(3) using LDA+DMFT provide insights into its electronic structure.
The method is shown to be relevant for understanding phenomena like the colossal magnetoresistance observed in doped manganites.

Conclusions:

LDA+DMFT offers a robust framework for ab initio electronic structure calculations of materials with strong electronic correlations.
The method advances the understanding of complex materials and their potential applications.
The study highlights the advantages and limitations of the LDA+DMFT approach for future research.