Computational Chemistry 4.2 - Atomic Units

Short lecture on the use of atomic units in the Hamiltonian operator of molecular systems.
Molecular systems exist at a very very small scale such that using SI units is very inconvenient, requiring scientific notation for expressing almost every value. Additionally, the molecular Hamiltonian is full of physical constants which make derivations tedious and error-prone. Both of these problems can be solved by the use of atomic units, where many common quantities are set to a value of 1, including the mass and charge of the electron, hbar, and the permittivity of free space. This gives a distance unit of Bohr, which is 0.529 Angstroms.
Notes Slide: i.imgur.com/229AXu1.png
-- About TMP Chem --
All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker.
Email: [e-mail]
-- Video Links --
Course Playlist: • Computational Chemistry
Chapter Playlist: • Hartree-Fock Theory
Other Courses: • PChem Course Intros
Channel Info: • About TMP Chem
-- Social Links --
Facebook: / tmpchem
Twitter: / tmpchem
LinkedIn: / tmpchem
Imgur: tmpchem.imgur.com
GitHub: www.github.com/tmpchem
-- Equipment --
Microphone: Blue Yeti USB Microphone
Drawing Tablet: Wacom Intuos Pen and Touch Small
Drawing Program: Autodesk Sketchbook Express
Screen Capture: Corel Visual Studio Pro X8

[@ibrahimnazemqader9153]

GREAT

[@Reox86]

I understand that substitution by 1 is conveninet but I fail to understand how is ℏ² equivalent to ℏ as 1² is equivalent to 1. The value 1 has special properties for the xⁿ operator that cannot be applied to other cases. Am I reading this wrong?

[@guacguc1]

As I understand it, the result gives hartree units. like 1m*1m = 1m^2. 1ħ*1ħ = 1ħ^2. the ħ^2 is not shown because he reduced the mathematical expression to include hartree units.

[@apburner1]

First.

[@TMPChem]

You're gonna be typing for quite a while to claim first on every upload from today.

[@apburner1]

Keep checking :)