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Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

Molecular Orbital Theory I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

Atomic Orbitals

Atomic Orbitals

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 I

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...

The Energies of Atomic Orbitals

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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Related Experiment Video

Updated: Jun 11, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

A Constraint-Based Orbital-Optimized Excited State Method (COOX).

Jörg Kussmann¹, Yannick Lemke¹, Anthea Weinbrenner¹

¹Chair of Theoretical Chemistry, Department of Chemistry, Ludwig-Maximilians-Universität in Munich (LMU), München D-81377, Germany.

Journal of Chemical Theory and Computation

|September 30, 2024

Summary

We developed a new computational method, COOX, for accurately calculating electronic excited states. This approach offers stable convergence and precise excited state densities, improving quantum chemistry simulations.

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Last Updated: Jun 11, 2025

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Area of Science:

Quantum Chemistry
Computational Spectroscopy
Electronic Structure Theory

Background:

Accurate calculation of electronic excited states is crucial for understanding photophysical and photochemical processes.
Traditional methods like linear-response time-dependent density functional theory (LR-TDDFT) can face challenges with convergence and accuracy for certain systems.
Constrained density functional theory (cDFT) offers a framework for enforcing specific properties during electronic structure calculations.

Purpose of the Study:

To introduce a novel method, the constraint-based orbital-optimized excited state (COOX) method, for direct calculation of targeted electronic excited states.
To provide a stable and accurate alternative to existing methods for computing excited states within a self-consistent field (SCF) framework.
To enable the application of post-SCF electron-correlation methods to excited states.

Main Methods:

Development of a novel constraint based on the difference density from simplified LR-TDDFT calculations.
Implementation of the COOX method within a self-consistent field (SCF) calculation.
Utilizing a restricted SCF approach for singlet excitations to prevent spin contamination and allow post-SCF treatments.

Main Results:

The COOX method demonstrates stable convergence behavior for excited state calculations.
Achieved accurate excited state densities that adhere to the Aufbau principle.
Demonstrated applicability to various systems, including benchmarks for excitation energies, excited state nuclear forces, structure optimizations, long-range charge transfer excitations, and conical intersections.

Conclusions:

The COOX method provides a robust and accurate approach for calculating electronic excited states.
The method's ability to yield accurate densities and facilitate post-SCF treatments opens new avenues for theoretical investigations.
COOX shows promise for studying complex phenomena like charge transfer and conical intersections.