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Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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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...

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Valence Bond Theory and Hybridized Orbitals

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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.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...

Atomic Orbitals

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Line, Surface, and Volume Integrals

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A line integral for a vector field is defined as the integral of the dot product of a vector function with an infinitesimal displacement vector along a prescribed path. If the prescribed path is closed, the integrals reduce to a closed-line integral. The closed-contour integral of the vector field is referred to in terms of the circulation of the vector field around the closed path. A vector with zero circulation around every closed path is called a conservative field, while one with non-zero...

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Related Experiment Video

Updated: Jun 8, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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Extending GPU-accelerated Gaussian integrals in the TeraChem software package to f type orbitals: Implementation and

Yuanheng Wang^1,2, Diptarka Hait^1,2, K Grace Johnson^1,2

¹Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA.

The Journal of Chemical Physics

|November 6, 2024

Summary

This study introduces f function support to the GPU-accelerated TeraChem software, enabling faster quantum chemical calculations. The enhanced software efficiently simulates large organic and transition metal systems.

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Published on: October 12, 2019

Area of Science:

Computational Chemistry
Quantum Chemistry
Materials Science

Background:

Graphics Processing Units (GPUs) offer potential for accelerating scientific computations.
High angular momentum basis functions in quantum chemistry can limit GPU acceleration efficiency.

Purpose of the Study:

To implement f function support in the GPU-accelerated TeraChem software package.
To enhance the efficiency of quantum chemical calculations for complex systems.

Main Methods:

Developed efficient kernels for Hamiltonian integral evaluation supporting f functions.
Utilized GPU acceleration within the TeraChem software.
Performed Density Functional Theory (DFT) and Coupled Cluster (CC) calculations.

Main Results:

Successfully implemented f function support, improving GPU acceleration.
Demonstrated high efficiency for large organic molecules and transition metal complexes.
Showcased applicability in DFT and CC calculations, including catalysis and photochemistry.

Conclusions:

The enhanced TeraChem software with f function support is well-suited for rapid simulation of large transition metal and organic systems.
GPU acceleration is effectively leveraged for complex quantum chemical computations.