The Evolution of Quantum Chemistry: From Pencil and Paper to Quantum Computing

When I was in high-school, I didn’t even know that something like quantum chemistry existed, “Quantum” was not a buzzword. I just wanted to become a scientist. The bubbles, the colors, the smells – I loved it all. But later, when I actually enrolled in an undergraduate chemistry course, I discovered that I wasn’t exactly what you’d call a “natural” in the lab. My experiments would always turn out differently than everyone else’s. Their solutions would be yellow and steaming, while mine would be brown and cold. They’d find aluminum in their samples, while I’d find iron. And then one day, after a couple of minor lab disasters, one involving fire and the other strong acids, my tutor sat me down and told me, “Arturo, you’re a great student and all, but you’re a calamity with the beakers. Have you ever considered switching to quantum chemistry?”

And switch I did. I graduated with a Ph.D. in quantum chemistry from the University of Cardiff (UK). But then, after years of academic research, life took me in a different direction, and I traveled the globe as an education manager within the medical device industry. Recently, I’ve returned to the world of quantum chemistry.

Why, you ask?

Well, the field has entered an exciting phase, with quantum chemistry becoming an indispensable tool in industries that are committed to saving the planetrenewable energy, carbon capture, energy storage. Plus, with the advent of quantum computing, the prospects for quantum chemistry have never been brighter.

This is not the first time that the field experiences a resurgence due to advances in computing power. As our old friend Giambattista Vico would say: Yeah man, history has a nasty habit of repeating itself.

Quantum Mechanics and Quantum Chemistry - Schrödinger

Quantum Chemistry: What is that?

There is a ton of resources out there, not all of it accurate. I will one day go into the thick of it, but for now, let’s just say this: Quantum Chemistry is a fancy name for a branch of physical chemistry that makes use of quantum mechanics, Schrödinger and co., to study chemical systems on an atomic level.

Quantum chemistry provides a rich and accurate amount of information about molecular structures and properties, spectra, thermodynamics, kinetics, and reactivity. It allows you to understand your system bottom-up, from atoms and electrons, to predict how molecules and materials behave.

So, how did we go from Schrödinger’s quantum mechanics to present day’s quantum chemistry?

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Pencil-and-Paper Quantum Mechanics

Usually, experts argue that the origins of quantum chemistry date back to the discovery of the Schrödinger equation in 1926. But, if you ask me, the real turning point didn’t come until a year later, when Walter Heitler and Fritz London published their trailblazing work.

Figure 1 from Heitler and London original paper - quantum chemistry

After weeks, probably months, of draining pencil-and-paper calculations, Walter and Fritz determined the change in energy experienced by two neutral hydrogen atoms as they approached each other (yup, the graph on the left is from the original paper). Data point by data point, they described the bonding of two hydrogen atoms into a molecule within the newly formulated quantum mechanical framework.

The story of this scientific breakthrough is quite technical, but it suffices to say that for the first time quantum mechanics was applied to the hydrogen molecule – pencil and paper illuminated the enigmatic phenomenon of chemical bonding.

Just like that, a whole new field of chemistry was born.

For a while, things looked pretty good for the romantic entanglement between quantum mechanics and chemistry; it seemed that a happy marriage was on the agenda. It was just a matter of solving the Schrödinger equation, and voila, you could predict molecular properties.

Not so fast, said Paul Adrien Maurice Dirac, the Englishman who, in his Ph.D. dissertation, introduced special relativity into Schrödinger’s equation and, in passing, predicted the existence of antimatter.

Ab initio means “from first principles”, implying that the only inputs into an ab initio calculation are physical constants. Ab initio quantum chemistry methods attempt to solve the electronic Schrödinger equation given the positions of the nuclei and the number of electrons in order to yield useful information such as electron densities, energies and other properties of the system.


Our genius friend Paul dropped a bombshell: quantum mechanics provides all that is necessary to explain problems in chemistry, but at a huge cost. Practical “ab initio calculations” for molecular systems are very hard – basically impossible by hands.

At that time, there were plenty of excellent minds and pencils and paper, but even with the sharpest minds and the finest pencils, those quantum mechanical calculations were so tedious to pose a daunting threat to the scientific community’s optimism.

And so, from that point forward, the history of quantum chemistry became a tale of folks trying to figure out how to make it work. A tale with protagonists such as Hartree, Slater, Coulson, Hund, Pople, Löwdin, Kohn, and many others. For decades, these pioneers tried to devise strategies to overcome the inherent difficulties of using quantum mechanics to explain chemical phenomena until finally, digital computers came along to save the day.

Diatomic Molecules – the first computer calculations

There were setbacks along the way, but scientists are untiring problem-solver machines, and finally success arrived in 1955.

30 years after Schrödinger, W.C. Scherr, a graduate student of future Nobel laureate Robert S. Mulliken, used computers to perform the first-ever all-electron ab initio calculation of a molecule larger than the hydrogen molecule. This achievement marked a major advancement in quantum chemistry and opened up new possibilities for understanding the behavior of larger molecules.

This story still blows my mind. Think about it. Using the brain-twisting principles of quantum mechanics, we input our molecular information into the Schrödinger equation to estimate electron properties. This enables us to predict the features of a molecular system with a high degree of accuracy, ranging from reasonable to, well, freaking spot on.

Let’s get real. It took Scherr two years (!) to complete those calculations, which included only two Nitrogen nuclei and 14 electrons. Two years, for quantum’s sake!

To be fair, eleven years after, the computation time went down to two minutes. Nowadays, we can run the same calculations in a matter of seconds.

That’s what progress looks like. We can now solve quantum problems faster than we can make a cup of coffee.

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The New Era of Quantum Chemistry

After this breakthrough and thanks to to the lightning-fast advances in computer tech, those soul-crushing days of staring at endless tables of molecular integrals and painstakingly interpolating values were starting to fade into obscurity. Enter a rad group of quantum chemists led by the legendary John Roothaan, joined by Platt and Rüdenberg, on a mission to develop the first generation of machine programs that could deal with diatomic wave functions.

Together they developed an innovative program using machine language for the UNIVAC computer – back when computer languages like Fortran were barely out of diapers. Problem was, the University of Chicago didn’t have the computing facilities to run the program. So what did they do? They snagged a sweet contract to use excess computer time at Wright Field Air Force Base in Dayton.

This crew of renegade quantum chemists made the trek to Dayton every few weeks for over 18 months, burning the midnight oil and chugging coffee, all to get their diatomic wave functions to run like clockwork.

Remember, we are in the late 50’s now, and what they pulled off is nothing short of incredible. I’m talking about going from manually crunching numbers for months, maybe years, to harnessing the raw power of state-of-the-art computer programs that could do the same calculations in mere minutes.

And the results? Oh my. Wow.

For the 12 diatomics studied, their computations underestimated energies by only 1% or less. Plus, they totally nailed the prediction of the sign and order of magnitude for dipole moments, estimated the ionization potentials with an accuracy of one figure, and provided correct order of magnitudes and one- to two-figure agreement for spectroscopic constants with respect to experiments.

Quantum chemistry demonstrated its value, marking a huge leap forward. It’s no surprise that after the program’s success, Robert S. Mulliken dubbed it the beginning of a new era.

Failure after failure and victory after victory, our short story catches up with the present day. Quantum chemistry started out as a hot mess that couldn’t offer analytical solutions to almost all of chemistry’s problems. Even though the equations were nicely written down, they were about as useful as a broken compass. But amidst this storm, a beacon of light appeared on the horizon: the computer.

This single instrument promised an unbounded frontier of numerical solutions, paving the way for quantum chemistry to become an essential tool in the modern chemist’s toolbox.

Further reading: Kostas Gavroglu and Ana Simões, Neither Physics nor Chemistry.

A final personal touch

There is so much to write about quantum chemistry, its history, the personalities who made it all possible. I have barely scratched the surface.

From the days in Arosa when Schrödinger wrote down his equation to tomorrow’s quantum algorithms, there has been an incredible progress. Quantum chemistry works, no doubt. And yet, there are many challenges to be addressed.

If we want to take quantum chemistry to the next level, we need to further develop our computational methods – fast, robust, and accurate enough to handle every chemical process, regardless of its state – gas, liquid, or solid.

Just like in the 50’s, will advancement in (quantum) computing come to help? How and when exactly? How will quantum chemistry look in 10, 20, 30 years?

After a detour of a few years, I’m excited to be back in the field. Quantum chemistry feels like home.

Let’s work together to create a quantum chemistry that every experimentalist can use, one that can be employed as a real predictive device that helps advance scientific research and human progress.

If you enjoyed this dive into the history of quantum chemistry, I’d love to hear your thoughts. Agree, disagree, or have a totally wild theory of your own? Let’s connect! Subscribe to my LinkedIn newsletter and let’s keep the conversation rolling.


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