Scientific research teams often use a computational model to better understand their system. In many areas, building these computational models is a full-time job, one that gives people long careers. These models can require advanced understanding of physics, chemistry and biology, and they often require careful and informed trade-offs between accuracy and computational speed.
This is especially true in chemistry, where the electrons that make everything work are governed by the quantum mechanical wave function. Computing for anything but the simplest atoms is impossible, but we often want to understand what electrons are up to in complex bulk materials.
Over the past few decades, researchers have built a variety of algorithms intended to produce an approximate result, usually based on concepts collectively referred to as “density functional theory.” But researchers have now shown that the most recent generations of algorithms have become extremely biased; they’re getting better at estimating the energy of the electrons, but maybe they will worse to get their geometry right. Ironically, the problem may be more reliance on empirical data for developing the software.
Density functional theory is common in chemistry and materials science work because it scales from single atoms to complex materials. It is used to estimate the behavior of electrons in these materials, which can be critical to understanding everything from their basic chemistry to their suitability for various electronic applications. The model offers a way of arriving at this data that does not face the impossibility of computing the wavefunctions of all electrons involved.
At the heart of density functional theory – the theoretical part of things – is the idea that there is a mathematical function that can relate the electron density distribution in a material to its energy. If you can minimize this function, you can produce the ground state of the system, getting both the energy and electron density, which tells you a lot about the chemical, physical, and electronic properties.
There is only one small catch: we have no idea what this feature is.
The applied science of density functional theory has found ways to approximate the function by balancing the computational intensity of the task against adding increasingly realistic physics to the behavior of the electrons. The assumption is that the more things you get right in the algorithm, the better it would reflect the actual behavior of a system.
A Russian-American team of researchers decided to test whether this assumption was correct. So they collected 128 different algorithms and ran them on a series of simple atoms and ions (things like a fluorine ion that has lost five electrons). These are so simple that another computational approach can provide a near-exact solution before the sun expands to engulf the Earth. The idea was to compare how well the different density functional theory algorithms approximated the relatively exact solutions.
For a while there was a clear trend: as the algorithms become more sophisticated over time, the algorithms can better describe the system. Both the energy and electron densities get closer and closer to the values produced by the more exact algorithm. But things changed shortly after 2000. After that, the energies estimated by these algorithms got better and better. In contrast, the estimated electron densities are starting to become actual worse.
Why could this happen? Ironically, it is more of a problem with algorithms based on empirical data. Instead of calculating everything based on physical principles, algorithms can replace some calculations with values or simple functions based on measurements of real systems (an approach called parameterization). However, relying on this approach seems to do bad things to the electron density values it produces. “Functionals constructed with little or no empiricism,” the authors write, “tend to produce more accurate electron densities than highly empirical ones.”
On some level, this is a clear departure from the ideas underlying the whole field: that you need to get both the energy and density distributions closer to the ground state.
But does it matter? In a guiding perspective, Sharon Hammes-Schiffer of the University of Illinois at Urbana-Champaign agrees that we should try to do better with both values. But she also notes that these issues need to be verified with more complex systems, such as whole molecules. She also suggests that current algorithms are still suitable for a number of applications. “For applications in chemistry, biology and physics, relative energies and geometries are often of primary importance,” she writes. “If the electron density does not affect these properties and is itself not of direct concern, then the imprecise electron density may not be relevant.”
Of course, researchers who have relied on these algorithms will want to step back and evaluate whether their system is one where electron density matters.
Science2016. DOI: 10.1126/science.aah5975 (About DOIs).