The Outline
Starts are often confusing, messy and come with a strong urge to procrastinate. And I am starting two things: studying about a new subject and presenting it in an unusual format.
Usually, while writing, you have a target audience in mind. Still confused about the style of writing that must be pursued, a simple question needs to be asked- Who is this being written for? The answer of excuse is knowledge transfer for the next researcher. How to visualise the unknown next researcher? Perhaps defaulting to my personality is a simple solution.
If that is the case, it becomes pretty clear how the article must be written: It cannot be a dry scientific discourse. Journal articles are read with as much attention as watching a marvel movie on a laptop- exciting in the beginning but you end up skipping important stuff. There is a need to make this a well thought out story with an interesting plotline and catchy subplots, rather than a write as you read sort of disorganised affair.
This makes a case to outline the chapters of the story, most of which, at this point are possibly unplanned and probably unknown. And so I sat down, opening a raft of webpages to feel well researched but ultimately going with wiki. Consuming the few first lines of the topic in question, and understanding it has something to do with finding the electronic structure of atoms and molecules through computer simulations. This is probably a good starting point.
Electrons interact with each other and with the nuclei through the coulomb interactions, which is because of the charges that they carry, and through other interactions known as exchange interaction and electronic correlation. Both exchange interaction and electronic correlation probably require separate posts of their own, for now we will just assume they are some mechanisms through which electrons “interact”, aka apply a force on each other. This distribution of electrons around the nuclei is the electronic structure we had initially mentioned.
In a system of electrons and nuclei contained in a volume in space, we can therefore see the problem begin to emerge as a problem of n-body dynamics. A lot of particles applying non-contact forces on each other. Something like our own solar system. Or universe. Since the particles are applying forces on each other, and these forces are dependent on the distance between the particles, there is an associated energy with every configuration in space of the given particles. What this means is, if the same particles are placed in different points in space each time, the potential energy of the entire system changes. Density Functional Theorem is one of the tools to determine which particular configuration results in the minimum energy, i.e. the ground state of the system.
This is equivalent to solving the Schrodinger's equation to determine the ground state wave function of the system. Which seems to be our main task. At this point, it becomes clear that we cannot proceed further without an understanding of what Schrodinger’s equation is. In a few borrowed words, Schrodinger’s equations is to quantum mechanics what Newton’s laws are to classical mechanics. They govern the dynamics of particles and are especially relevant in quantum systems. Unfortunately, my appetite of writing is fulfilled for the day, and Schrodinger will have to wait for the next post.
All in all, we will do the following in the subsequent writings:
- understand what the schrodinger’s equation is all about
- understand the nature of interactions between electrons
- look at Hartree-Fock methods, competitor and predecessor
- understand how density functional theorem actually works
- posts once we start to understand how DFT actually works
With this, we conclude the outline.