The objects you interact with every day are predictable – you can pick up a box, sit down in a chair without falling to the floor, or open a door without your hand passing through the knob. But if you zoom in on these objects all the way to the quantum level – where you look at the individual atoms – you’ll find that things start to behave somewhat strangely.

The typical size of quantum objects is a nanometer, or one-billionth of a meter. For scale, a human hair is 60,000-100,000 nanometers wide. At the nanoscale level, you cannot know where exactly a particle is in space – you can only calculate a probability of where it might be.

At the quantum level, particles exhibit wavelike behavior. Instead of discrete, tiny objects, particles act more like continuous waves. A particle’s properties, including properties as basic as its position in space, are defined in terms of probabilities. You can’t know exactly where the particle is, but you can estimate the chances of finding it within a certain region of space. You can compute these probabilities using Schrödinger’s equation, the solutions to which are called wave functions.

About a century ago in 1926, Austrian physicist Erwin Schrödinger developed the wave equation, which allowed him to calculate the probability that a particle exhibited a certain property from its wave functions.

Even though the human eye can’t parse what’s happening at the quantum scale, the way particles behave at that level influences how you experience the world. It gives plants their green color, provides the foundations for computer and information technology, and governs how many everyday materials work.

The wave equation and wave functions

I am a theoretical chemist, and Schrödinger’s 100-year-old breakthrough equation underlies many of my research projects. I track how atoms in certain chemicals are rearranged when they react with one another. Following chemical reactions at such a tiny scale can help researchers develop more efficient reactions, which is useful for everything from creating biofuels to developing solar energy technology.

How atoms behave at the quantum level dictates the properties molecules and materials have, so understanding their wave functions is key, and Schrödinger’s formulation became widely used for this purpose. Scientists try to compute these wave functions before synthesizing and characterizing the molecules directly in the lab, so the labs can focus their resources on the most promising reactions.

However, the Schrödinger equation is impossible to solve exactly, even on supercomputers, for all but the smallest molecules consisting of up to five or six atoms. This is because the difficulty of computing the wave function scales exponentially with bigger molecules. So if I need to calculate 10 bits of information per quantum particle, I will need 100 bits for two interacting particles, 1,000 bits for three particles, and so on.

To predict the properties of larger molecules and materials, researchers have developed methods that can find approximate wave functions. These techniques help scientists design new molecules and materials with specific desired properties for use in, for example, better sunscreens, solar cells, biodegradable plastics or nanoparticles for drug delivery.

Nowadays, you can solve the Schrödinger equation for electrons using well-established commercial or free software. If your molecule of interest is not too large – a few dozen atoms – you can quickly compute information about it, such as how stable it is or what wavelength of light it will absorb.

But these tools are limited. To understand quantum effects present in larger molecules, you’ll need a specialized set of tools, which my colleagues and I develop.

Quantum effects in chemical reactions

One effect that comes into play at the quantum level, called quantum tunneling, can change how certain chemical reactions play out. Wave function solutions take this effect into account.

During many chemical reactions, the initial set of molecules, called reactants, have to overcome an energy barrier as their atoms are rearranged into the products of the reaction. Typically, this type of reaction would only take place if the reactants were heated up enough that they could sail above the barrier and release their energy on the product side.

But sometimes, for reactions at the quantum level, there is a chance the molecules can react even if their total energy is lower than the energy barrier. This phenomenon is called quantum tunneling. At low temperatures with light atoms, it can be the only way to have the reaction. Lighter particles have wave functions that are more spread out in space – these are more likely to exhibit quantum effects.

The lightest atomic nuclei are found in hydrogen atoms, and these are the most inclined to quantum tunneling. If hydrogen atoms are involved in a chemical reaction, scientists can use this tunneling property to learn certain details about the reaction. They do so by replacing some hydrogen atoms with a heavier version, called deuterium. Deuterium has a neutron in its nucleus, which hydrogen doesn’t, so it’s twice as heavy and less able to tunnel.

Experiments with quantum tunneling

In 2022, my colleagues and I examined hydrogen atom transfer for a reaction that is part of the process that converts a sustainable biological resource, such as straw and switchgrass, into liquid fuel, such as gasoline and diesel. Our quantum calculations told us that a hydrogen atom was tunneling, which increased the reaction’s efficiency. The tunneling atom meant the reaction could still take place, even with a low-energy input. Over time, this small factor led to real efficiency gains.

Our work explained how making a minor modification to a reacting molecule – switching the hydrogen to deuterium – could increase the size of the energy barrier and stop tunneling. Because of these quantum behavior quirks, even a seemingly small change can stop the reaction altogether.

Future quantum applications

Some technological applications that take advantage of particles’ quantum behaviors are truly futuristic, such as quantum computers. Quantum computers could eventually solve very demanding computational problems much faster than regular computers.

Right now, we have only early prototypes of quantum computers, which are large, highly complicated experimental machines – not unlike early computers that were the size of a room.

Perhaps quantum computers could one day help scientists solve the Schrödinger equation for molecules made up of thousands of atoms so we can design better molecules, materials and technologies.

Sophya Garashchuk receives funding from the National Science Foundation and Department of Energy of USA.