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Valence Bond Theory

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...

Valence Bond Theory

Valence Bond Theory

Overview of Valence Bond Theory

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

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...

Valence Bond Theory and Hybridized Orbitals

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...

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Updated: Dec 25, 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

Natural transition orbitals for complex two-component excited state calculations.

Joseph M Kasper¹, Xiaosong Li¹

¹Department of Chemistry, University of Washington, Seattle, Washington, USA.

Journal of Computational Chemistry

|March 29, 2020

Summary

This study extends the natural transition orbital (NTO) method to two-component molecular orbitals, enabling visualization of electronic excitations in complex systems. The new approach explicitly handles spin and spin-flip transitions.

Keywords:

TDDFT generalized Hartree-Fock generalized Kohn-Sham natural transition orbitals relativistic methods two-component electronic structure method

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Last Updated: Dec 25, 2025

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Area of Science:

Quantum Chemistry
Computational Chemistry
Theoretical Chemistry

Background:

The natural transition orbital (NTO) method simplifies electronic excitations in time-dependent Hartree-Fock and density functional theory.
Extending NTOs to multicomponent molecular orbitals (e.g., relativistic two-component, generalized Hartree-Fock/Kohn-Sham) is challenging due to spin-component mixing and spin-flip transitions.

Purpose of the Study:

To extend the single-component natural transition orbital (NTO) method to a two-component framework.
To address the complexities of spin-component mixing and spin-flip transitions in generalized Hartree-Fock/Kohn-Sham methods.

Main Methods:

Development of a two-component natural transition orbital (NTO) method.
Discussion of practical aspects for visualizing two-component complex orbitals.
Application of the method to calculations on a mercury atom and a CrO2Cl2 complex.

Main Results:

The extended NTO method successfully visualizes electronic excitations within a two-component framework.
The method explicitly accounts for spin, often yielding multiple significant orbital pairs.
Successful application demonstrated on a mercury atom and a CrO2Cl2 complex.

Conclusions:

The presented two-component NTO method provides a valuable tool for analyzing electronic excitations in relativistic and generalized electronic structure calculations.
This extension facilitates a more intuitive understanding of complex electronic transitions involving spin.