Getting Solid Predictions: Reliable Calculations of the Thermodynamic Properties of Crystalline Matter

The thermodynamic properties of a substance express fundamental insights into how energy is contained within, and transferred to, the substance. The thermodynamic properties therefore relay crucial information about how a substance behaves in response to heat and work and in the context of other substances. Countless chemical processes are therefore reliant on, and affected by, the thermodynamic properties of substances. Despite this, we have only measured thermodynamic properties of a fraction of known crystalline solids and of this fraction, the measured thermodynamic data is often sparse. Furthermore, the rate at which new experimental thermodynamic data is determined continues to be considerably slower than the rate of crystal discovery. To address this, various predictive models have been developed and used to fill in the knowledge gaps.

For a long time, predictive models for solid thermodynamic properties were only practical if they were based on empirical rules. Generally, these empirical models were flawed because they were only reasonably accurate for small sets of compounds. The physical theories for the thermodynamic properties of solids from an atomistic view were already mature a century ago but the computational tools to accurately and efficiently apply them were not. Therefore, predictive models for the thermodynamic properties of solids had only limited success in application. In recent decades, computing power has grown immensely and physical computational theories have evolved concurrently. This has enabled much more powerful thermodynamic modeling of solids. Nonetheless, the physical models still face challenges in practical use due to their considerable computational requirements, complexity and systematic errors stemming from their underlying approximations.

In this work, we have investigated various approaches to thermodynamic modelling of solids and arrived at a prediction framework based on atomistic models, which strikes an effective balance between accuracy, speed and flexibility. To model their temperature-dependence, we have considered models of lattice dynamics and found that the harmonic approximation (HA) performs satisfactorily in many circumstances when compared to more advanced methods. The simplicity and computational low-cost of the HA makes it a very valuable tool for efficient thermodynamic property prediction. The underlying atomistic model that was chosen for these calculations is density functional theory (DFT). Unfortunately, the approximations which, are necessary to construct DFT methods, result in a mediocre description of the thermodynamic formation properties of solids. In order to tackle this issue, we have developed and benchmarked an approach based on reaction network (RN) theory. Using compiled experimental data and DFT calculations, we can effectively cancel the systematic errors which plague the DFT calculations to obtain accurate predictions for the thermodynamic formation properties. Because of its construction, the RN provides considerable insight into the predictions, including e.g. uncertainty analysis and i allows for many adjustments which can further improve its predictions. During the span of our work exceedingly accurate machine learning interatomic potentials (MLIP), trained on DFT data have been developed. In our final investigation, we combine MLIP-based HA calculations with RN predictions to obtain temperature-dependent predictions of thermodynamic properties for a large number of solids. We find that this methodology provides a useful compromise between the aforementioned accuracy, speed and flexibility. All the components of this prediction framework can be replaced or developed in a rational way to make further improvements and adaptations as methods improve to suit specific applications.