Research

Quantum Chemistry – Better Than a Magic Trick

Think about a molecule you know from your chemistry classes. Don’t tell us the name, don’t tell us its properties, don’t show us the IR or NMR spectrum you measured, do not even show us where the bonds are. Instead, for a second, imagine you could strip off all electrons and stow them away in your pocket. What is left? Just a collection of positive atomic nuclei at different positions in space. Now, imagine a 3D coordinate system, that is, an x-axis, y-axis, and z-axis, and write down the coordinates of these nuclear positions and the number of positive charges at each position in space. Now comes the “magic trick”: If you just tell us these coordinates and how many electrons you have in your pocket, we will use Quantum Chemistry to tell you everything about your original molecule: where the electrons would be, where and what type of bonds are formed, what its properties are, and even predict the IR, NMR, or UV-Vis spectra.

Computational Chemistry

Well… at least in a few hours or next week. That’s because the mathematical equations we need to solve to make all these predictions are impossible to solve with pen and paper. Instead, we rely on numerical computer algorithms to solve them, and this can take a very long time depending on how large your molecule is or how accurate you would like the prediction to be. That’s also why we do not use a regular laptop computer but instead use a High Performance Computing (HPC) cluster, which offers more than 100 times the computational power of a regular laptop and can run 24/7.

Using these computer programs, we can just sketch molecules on the computer, provide the program with the coordinate file and enter the number of electrons, and calculate virtually every property chemists, pharmaceutical researchers, or materials scientists could be interested in. Imagine the possibilities: we can understand reaction mechanisms, predict molecular properties, design new materials, predict activation and reaction energies, understand why some reactions occur readily while others do not, we can even screen thousands of potential materials or drug candidates before synthesis, saving considerable time and resources in the laboratory.

Sounds too good to be true – what’s the catch?

If magic worked, nobody would be doing science. So what’s the catch and why is everyone not just using Computational Quantum Chemistry magically making groundbreaking discoveries from the convenience of their desk (or bed…)? The big big problem is that the increase in computational time for the numerically exact solution already mentioned above is so extreme that all but the smallest systems (think: \(\mathrm{H_2O}, \mathrm{CO}\)) can be treated exactly. The computational effort scales factorially with the number of electrons, so calculating two water molecules (20 electrons) instead of one (10 electrons) already takes \( \frac{20!}{10!} = 670,442,572,800\) times longer. If you think next year’s computers will solve this, add a third water molecule and you are looking at a factor of \( \frac{30!}{10!} =73,096,577,329,197,271,449,600,000\). Computers alone cannot win this battle!

The research objective of quantum chemists is thus to develop, implement, validate, and apply approximate methods that give approximate yet useful results in reasonable computational times (minutes to a few weeks). One of these methods that we study in the Grotjahn Lab is Density Functional Theory (DFT). This method has revolutionized chemistry and is a major reason why Computational Chemistry is so widespread nowadays.

This also means that Computational Chemistry does not replace experiments. In practice, it acts as a guide for new ideas, helps with the interpretation of experimental measurements, unravels steps that experimental techniques cannot resolve, or makes testable predictions. That’s why the Grotjahn Lab is involved in various projects covering many areas and applications of chemistry. Often the best part of this research is when you see a method you have developed and tested for years actually helps another chemist to understand the molecules they are working on.