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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 II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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.

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Molecular Orbital Theory II

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Related Experiment Video

Updated: Mar 29, 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

Projected Coupled Cluster Amplitudes from a Different Basis Set As Initial Guess.

Marco Caricato¹, Gary W Trucks¹, Michael J Frisch¹

¹Gaussian, Inc., 340 Quinnipiac St. Bldg. 40, Wallingford, Connecticut 06492, United States.

Journal of Chemical Theory and Computation

|November 26, 2015

Summary

This study introduces a novel method for accelerating coupled cluster (CC) calculations by using corresponding orbitals to generate better initial guesses. This approach significantly reduces computational time and cycles needed for convergence in quantum chemistry.

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Area of Science:

Quantum Chemistry
Computational Chemistry
Theoretical Chemistry

Background:

High-level calculations, such as coupled cluster (CC) methods, are crucial in computational chemistry.
The efficiency of iterative CC equation solvers heavily relies on the quality of the initial guess.
Standard initial guesses can slow down convergence, increasing computational cost.

Purpose of the Study:

To develop an improved strategy for generating initial guesses in CC calculations.
To leverage previous CC calculation results with different basis sets for a more efficient starting point.
To reduce the number of iterative cycles required for convergence.

Main Methods:

Employing the concept of corresponding orbitals to link results from previous CC calculations.
Projecting converged amplitudes from a prior calculation that correspond to the new basis set space.
Utilizing this projection as a new, improved initial guess for subsequent calculations.

Main Results:

The proposed method significantly reduces the number of iterative cycles needed for convergence.
Computational time for generating the guess is negligible.
Demonstrated effectiveness for ground and excited state calculations using CCSD and EOM-CCSD methods.
Validated with restricted and unrestricted Hartree-Fock reference functions.

Conclusions:

The corresponding orbitals approach provides a superior initial guess for CC calculations compared to standard methods.
This strategy offers substantial computational savings without significant overhead.
The method is general and applicable to various CC expansions and reference functions.