Thread by @realscientists

So, what is computational chemistry?! The field itself is a subfield of chemistry, incorporating aspects of theoretical chemistry / physics and computer simulations. This allows us as scientists to accurately describe (and predict) the properties of atoms and molecules.

Computational chemistry is broad and draws on many areas of science, notably quantum mechanics (QM), classical mechanics, and thermodynamics. We often draw (both directly and indirectly) on all three of these areas to answer a specific scientific question.

For example, let's say we want to describe the breaking of chemical bonds in a molecule during a chemical reaction. Here it is appropriate to use QM to accurately describe the energies involved with the exchange of electrons.

In this thread we'll dive into QM!

Quantum mechanics is, unsurprisingly, complex.

The central idea is that a particle (e.g. an electron) can be described as both a particle and a wave. How do we go about capturing this wave-like nature?

We can use a mathematical object called a wavefunction (WF), often denoted by the symbol psi (Ψ). The WF tells us everything we need to know about our system. Specifically, it tells us the probability amplitude of finding a particle in a certain space at a certain time.

If we square the WF* we find the real probability of a particle being in a certain place (before being squared the WF contains imaginary numbers!).

* technically we actually take the complex conjugate 👀

The WF is one of our best tools for describing quantum systems.

Ok, but how do we find out how our system evolves over time?

We use the Schrödinger equation (SE)!

The SE (shown below) tells us how our WF will evolve over time. It's made up of three main terms:

H (with a ^) is the Hamiltonian and this describes the total energy of the system. It formally "operates" on the WF.

Ψ is our WF from before. It's now inside what is called a "ket"* that just reduces some of the complex mathematical notation.

* en.wikipedia.org/wiki/Bra%E2%80…

E is known as the eigenvalue of this equation and corresponds to an experimental observable. In QM these values can only take certain, discreet, values.

I've simplified a lot there, but if you'd like to dig a little deeper into the maths do check out some great videos from @3blue1brown

QM (in the context of light):

Eigenvectors and eigenvalues:

It turns our that the Hamiltonian isn't just a simple "H", it has a rather complex form. The Hamiltonian for the electronic WF is shown below (don't panic!):

Let's go through this together.

The first term describes the kinetic energy of our system, the second term describes electron - nuclear attraction, and the third term describes electron - electron repulsion.

Ok, it's still pretty scary but luckily the complexity of these equations can be reduced by decoupling the molecular system into electronic and nuclear parts. This is known as applying the Born-Oppenheimer (BO) approximation.

This basically exploits the fact that electrons have less mass than the nuclei and so move whilst the nuclei essentially stay still! This is good, it means we have less moving parts to consider in our calculations!

Well done for making it this far! We're past the hard part.
Next up, how can we use computers to take advantage of the concepts described above? It turns out applying the BO helps a lot to develop computer code to solve problems involving the electronic WF.

A group of these methods are called ab initio (fancy latin for "from the beginning") methods. These work exclusively with the WF. One of the most well known ones is Hartree-Fock (HF) and although good, it doesn't take into account the correlated motion of electrons.

Just thinking back to our example, if we're trying to describe bond breaking then we need to model the correlated motion of electrons!

The use of Coupled Cluster (CC) methods does take this into account and is often seen as the gold standard for the calculation of molecule properties, but it is very expensive in terms of computational cost.

Another method uses just the electron density, motivated from the earlier point that the WF squared tells us all about the electron density surrounding a molecule. The benefit here is that it is much cheaper to run and so we can get results faster, with a trade-off for accuracy.

Finally, there are other methods that include adding in some experimental data (known as semi-empirical) as well as fancy methods that treat one part of a molecule with QM and the rest with classical mechanics (often used if you want high accuracy in one part of your system).

Phew! We made it. That was a whistle stop tour of QM in computational chemistry. In my next thread we will dive into molecular dynamics!

That can wait until after lunch...

(apologies for any typos!)

(urgh, as is always the case you spot errors after the tweet. When we "square" the WF we MULTIPLY by its complex conjugate)