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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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Electron Orbital Model

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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.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...

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Mutagenesis and Functional Selection Protocols for Directed Evolution of Proteins in E. coli

Mutagenesis and Functional Selection Protocols for Directed Evolution of Proteins in E. coli

Published on: March 16, 2011

Direct orbital selection for projection-based embedding.

Moritz Bensberg¹, Johannes Neugebauer¹

¹Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany.

The Journal of Chemical Physics

|June 10, 2019

Summary

This summary is machine-generated.

This study introduces an automated method for selecting active orbitals in projection-based embedding (PbE) for chemical reactions. This approach improves accuracy in calculating reaction energies and barriers without needing to specify active atoms.

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Area of Science:

Computational Chemistry
Quantum Chemistry
Method Development

Background:

Projection-based embedding (PbE) is a robust method for accurate electronic structure calculations.
PbE combines sophisticated methods for reaction centers with cost-effective DFT for environments.
Current PbE methods often require manual selection of 'active atoms'.

Purpose of the Study:

To develop an automated, inexpensive approach for selecting active orbitals in PbE.
To eliminate the need for specifying 'active atoms' in PbE calculations.
To investigate and compare different orbital selection schemes for PbE.

Main Methods:

Developed an automatic orbital selection strategy based on orbital changes during a reaction.
Applied the method to PBE0-in-PBE embedding, comparing variants based on orbitalwise partial charges and kinetic energy.
Evaluated performance using shellwise intrinsic atomic orbital charges for six different reaction types.

Main Results:

The proposed automatic orbital selection method effectively identifies orbitals active during a reaction.
Shellwise intrinsic atomic orbital charges proved to be the most successful selection scheme.
Errors in calculated reaction energies and barriers rapidly decreased as the active orbital space expanded.

Conclusions:

The automated orbital selection approach is a significant improvement over atom-based selection in PbE.
This method enhances the accuracy and efficiency of reaction barrier and energy calculations.
The findings pave the way for more accessible and reliable computational chemistry studies.