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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.

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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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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.
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Updated: Apr 9, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

Development of Local Natural Orbital Arbitrary Order Coupled Cluster Methods and Assessment through Connected

Vladimir Fishman¹, Balázs D Lőrincz^2,3,4, Emmanouil Semidalas^1,5

¹Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Reḥovot 7610001, Israel.

The Journal of Physical Chemistry. A

|April 8, 2026

Summary

We developed local natural orbital (LNO)-based coupled cluster (CC) methods for accurate quantum chemistry. These methods enable precise calculations of molecular energies for larger systems, advancing computational chemistry.

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Area of Science:

Quantum Chemistry
Computational Chemistry
Theoretical Chemistry

Background:

Coupled cluster (CC) methods are essential for accurate electronic structure calculations.
Higher-order CC methods like CCSDTQ provide high accuracy but are computationally expensive.
Local Natural Orbital (LNO) approximations offer a path to reduce computational cost.

Purpose of the Study:

To develop and assess LNO-based arbitrary order CC methods.
To rigorously evaluate the accuracy of beyond CCSD(T) correlation using LNO-CCSDTQ.
To enable accurate calculations for larger molecular systems.

Main Methods:

Development of closed- and open-shell LNO-based CC methods.
Implementation of an asymptotically linear-scaling framework.
Utilizing multilevel embedding and point group symmetry support.

Main Results:

LNO approximations achieve reliable accuracy (85-95% relative) for post-CCSD(T) contributions.
Accurate thermochemistry and noncovalent interaction calculations are demonstrated.
An unprecedented CCSDT(Q)-CCSD(T) reaction energy correction for an enzyme reaction was computed.

Conclusions:

LNO approximation significantly expands the applicability of high-order CC methods.
Enables kJ/mol accuracy for practical, large 3D molecular systems.
Facilitates advanced computational protocols in quantum chemistry.