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Molecular Orbital Theory I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

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...

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

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

MO Theory and Covalent Bonding

MO Theory and Covalent Bonding

The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

Method-independent cusps for atomic orbitals in quantum Monte Carlo.

Trine Kay Quady¹, Sonja Bumann^1,2, Eric Neuscamman^1,2

¹Department of Chemistry, University of California, Berkeley, California 94720, USA.

The Journal of Chemical Physics

|March 10, 2025

Summary

We developed a new method to improve Gaussian atomic orbitals by adding nuclear cusps. This approach is independent of the many-body method, offering statistical advantages for quantum Monte Carlo simulations.

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Area of Science:

Computational chemistry
Quantum mechanics
Materials science

Background:

Gaussian atomic orbitals are fundamental in computational chemistry.
Accurate representation of electron behavior near the nucleus (cusps) is crucial for precise quantum mechanical calculations.
Existing cusp correction methods can be dependent on specific many-body techniques.

Purpose of the Study:

To introduce a novel method for augmenting Gaussian atomic orbitals with accurate nuclear cusps.
To develop a cusp correction approach that is independent of the many-body method used.
To demonstrate the statistical benefits of these cusp-corrected orbitals in quantum Monte Carlo simulations.

Main Methods:

Augmenting standard Gaussian atomic orbitals with explicit nuclear cusp functions.
Ensuring the cusp-corrected atomic orbitals are uniquely defined by the basis set and molecular geometry.
Applying the method in quantum Monte Carlo calculations for various molecular systems.

Main Results:

The proposed method successfully incorporates correct nuclear cusps into Gaussian atomic orbitals.
The cusp correction is independent of the chosen density functionals, quantum chemistry methods, or variational Monte Carlo optimizations.
Statistical improvements were observed in molecular calculations, comparable to molecular-orbital-based approaches.

Conclusions:

The developed method provides a robust and versatile way to enhance Gaussian atomic orbitals with nuclear cusps.
This approach offers significant statistical advantages in quantum Monte Carlo simulations.
The method's independence from specific many-body techniques makes it broadly applicable in computational quantum chemistry.