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Molecular Orbital Theory II

Molecular Orbital Theory II

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Molecular Orbital Theory I

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Overview of Molecular Orbital Theory

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...

Atomic Orbitals

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An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

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Updated: May 5, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Orbital-optimized density cumulant functional theory.

Alexander Yu Sokolov¹, Henry F Schaefer

¹Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA.

The Journal of Chemical Physics

|December 3, 2013

Summary

This summary is machine-generated.

Density Cumulant Functional Theory (DCFT) now features orbital optimization for improved electronic energy calculations. This new formulation enhances dynamic correlation and simplifies gradient computations in quantum chemistry.

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Area of Science:

Quantum Chemistry
Computational Chemistry
Electronic Structure Theory

Background:

Density Cumulant Functional Theory (DCFT) offers an alternative to wavefunction computations for electronic energy.
DCFT decomposes the one-particle density matrix into mean-field and correlation components.
Previous DCFT formulations used orbital diagonalization, leading to partial orbital relaxation.

Purpose of the Study:

Introduce a new orbital-optimized formulation of DCFT.
Improve the description of dynamic correlation.
Simplify the computation of analytic gradients.

Main Methods:

Developed a variational minimization of energy with respect to orbital rotations.
Derived expressions for analytic gradients within the new formulation.
Analyzed new orbital stationarity conditions perturbatively.

Main Results:

The orbital-optimized DCFT formulation yields significant energy contributions.
Markedly improved description of dynamic correlation was achieved.
Analytic gradient computations are greatly simplified.

Conclusions:

The orbital-optimized DCFT presents a significant advancement in electronic structure calculations.
This method enhances accuracy in describing dynamic correlation.
The simplified gradient computations facilitate broader application in chemical systems.