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Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
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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: Apr 27, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

A method of orbital analysis for large-scale first-principles simulations.

Tsukuru Ohwaki¹, Minoru Otani², Taisuke Ozaki³

¹Advanced Materials Laboratory, Nissan Research Center, Nissan Motor Co., Ltd., 1 Natsushima-cho, Yokosuka, Kanagawa 237-8523, Japan.

The Journal of Chemical Physics

|July 3, 2014

Summary

A new method efficiently calculates natural bond orbitals (NBOs) for large systems using density matrix truncation. This enables localized chemical bond analysis in complex simulations, advancing computational chemistry.

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Published on: October 12, 2019

Area of Science:

Computational Chemistry
Materials Science
Quantum Mechanics

Background:

Accurate analysis of chemical reactions in large-scale systems is computationally demanding.
Traditional methods struggle to provide localized chemical bond insights for complex systems.
Natural Bond Orbitals (NBOs) offer a chemically intuitive description of electronic structure.

Purpose of the Study:

To develop an efficient method for calculating NBOs in large-scale systems.
To enable quantitative analysis of chemical reactions using localized Lewis-type bonds.
To integrate NBO analysis with O(N) electronic structure methods.

Main Methods:

A novel NBO calculation method based on density matrix truncation.
Utilizes O(N) electronic structure methods or exact diagonalization to compute the density matrix.
Achieves O(1) computational cost for NBOs in a local region of interest.

Main Results:

The method successfully recovers an orbital picture for O(N) methods.
Enables quantitative analysis of chemical reactions in large systems.
Demonstrated application in a large-scale first-principles molecular dynamics simulation of a liquid electrolyte.

Conclusions:

The developed NBO calculation method is efficient and accurate for large-scale systems.
It provides a powerful tool for analyzing chemical reactions and electronic structure.
Facilitates detailed chemical insights in complex materials and molecular dynamics simulations.