# What are some of the applications of computational chemistry?

Mar 3, 2016

Some applications I found on the ACS website, and some others that I just know of, include:

And more!

You can read below for more of an introduction to computational chemistry and its goals and challenges.

INTRODUCTION TO COMPUTATIONAL CHEMISTRY

Computational chemistry is a field of chemistry that I'm working in, and it involves using high-powered computers to do calculations that would normally take human beings way too long to do on paper, or even for the examination of molecules that are difficult to observe in real life.

On a semi-basic level, we could calculate things like entropy, enthalpy, specific heat capacity, vibrational frequencies, ground-state energy, etc.

The most common equation solved in this field is the Schrodinger equation, which contains $\psi$, the wave function which represents a quantum mechanical system, such as an atom or molecule.

$\hat{H} \psi = E \psi$

It just so happens that to solve this equation, we can write linear combinations using the wave function $\psi$.

HOW MIGHT WE TREAT THIS?

For instance, take this linear combination of atomic orbitals to generate molecular orbitals:

color(blue)(psi_("MO") = sum_(i=1)^(n) c_iphi_i^"AO" = c_1phi_1^"AO" + c_2phi_2^"AO" + . . . + c_nphi_n^"AO")

where:

• ${\psi}_{\text{MO}}$ is the wave function which represents a molecular orbital.
• ${\phi}_{i}$ is each experimentally-determined trial function that is generally solved to be of the form ${e}^{\pm \alpha x}$.
• ${c}_{i}$ is the expansion coefficient. There exists exactly one set of ${c}_{i}$ such that the linear combination has a particular solution.

And there exist many more for each type of molecular orbital (${\sigma}_{2 s}$, ${\pi}_{2 p x}$, etc). So we might have something like this as a basic example to solve:

${\psi}_{{\pi}_{2 p x}} = {c}_{1} {\phi}_{2 p x A} + {c}_{2} {\phi}_{2 p x B}$
${\psi}_{{\pi}_{2 p y}} = {c}_{3} {\phi}_{2 p y A} + {c}_{4} {\phi}_{2 p y B}$
${\psi}_{{\sigma}_{2 p z}} = {c}_{5} {\phi}_{2 s A} + {c}_{6} {\phi}_{2 p z B}$

(Don't think that looks easy? It isn't. Many algorithms require looping and performing trial and error calculations to solve gigantic systems of equations, which can get extremely intensive.)

In computational chemistry, it is useful to solve systems of equations like this (one equation for each molecular orbital) using matrices and taking the determinant. An example of a matrix is $\left[\begin{matrix}2 & 0 \\ 4 & 7\end{matrix}\right]$, and its determinant would be $2 \cdot 7 - 4 \cdot 0 = 14$.

THE COMPUTATIONAL DESIGN CHALLENGE

Solving matrices of higher order (larger dimension) gets increasingly harder and harder, and we resort to programming high-powered computers to do so in as efficient a way as we can write for the computer to utilize.

Sometimes calculations can take hours, and sometimes they can take days, depending on the size of the molecule. Having even 18 molecular orbitals (e.g. tetracene) can be taxing on many computers.

For instance, computing the wave function for a 54-orbital graphene sheet (which makes a good semiconductor) like (5a,4z)-periacene would be literally impossible for as long as we live with the methods we have now. I'm working on a method right now to get around that barrier.

Because of the way computational chemistry generalizes its variables to make it easier for the computer to use in multiple scenarios, it places an obligation on the computational chemist to program the computer to do the calculations consistently as well.

Therefore, the main goal of computational chemistry is to consistently calculate molecular properties in as efficient and quick, yet accurate a way as possible.