Lessons Lesson 4
Lesson 4 - Details on DFT Geometry Optimization
Written by Jeremy Schroeder
Introduction
As seen in the previous lesson, calculating the energy of the structure and optimization of structures is complicated. I used the Molecular Mechanics (MM) example to show equations and hopefully have a more sinplified understanding of the logic because as you increase the level of theory, the complicatedness and logic become more abstract. To understand every inner logic and workings of DFT would take years of math, quantum mechanics and chemistry classes to truly understand. So In this lesson I will show an example and particular steps of how DFT works.
Pauli-Exclusion Principle
How electrons are assigned in each orbital.
Calculated Orbital Energies and Locations
Click through to see each orbital energy of a water molecule that the program Orca found. These pictures are from the visulization program JMol and you can also use Molden or GaussView to see orbitals visualized.
Try to identify the LUMO (Lowest Unoccupied Molecular Orbital) and the HOMO (Highest Occupied Molecular Orbital). You can also find the Energy Gap which is the equation below.
\(E_{gap} = LUMO - HOMO\)
When looking at the pictures, the Red atom is Oxygen, the White atoms are Hydrogens, the red transparent cloud is the "positive" orbitals and the blue transparent cloud are the "negative" orbitals.
- The reason "positive" and "negative" are in quotations is that it's really two electrons that have opposite spin of each other and are not attracted to each other. Think like spin-up and spin-down.
This website linked below goes into more details about the orbitals a water molecule has.
HOMO is Orbital 5, with energy -0.28665087 H LUMO is Orbital 6, with energy 0.068232216 H So \(E_{gap} = 0.354883086\) H