Overcoming Distrust in Solid State Simulations: Adding Error Bars to Computational Data

Abstract

Simulation techniques are providing with each passing day a deeper insight into the structure and properties of materials. Two main obstacles appear for the cooperation of simulation and experiment: on the one hand, the frequent lack of a degree of uncertainty associated with calculated data. On the other, the concomitant underlying feeling that calculation parameters can be tuned with the explicit aim of matching the experimental results, even at the expense of the quality of the simulation. Without the definition of an error bar for estimating the precision of the calculation, direct comparison of calculated and experimental data can lack physical significance. In this contribution, we employ the well known delocalization error of DFT and HF to develop a simple and robust procedure to quickly estimate an error bar for calculated quantities in the field of solid state chemistry. First, we validate our model on one of the simplest properties of a solid, the geometry of its unit cell, which can be determined experimentally with high accuracy. In this case, our computational window is too large to provide a useful error bar. However, it provides computational material scientists with a pointer on how much a given system is affected by the method of choice, i.e. how much it is sensible to parameter tuning and how much care should be taken in doing it. Then, we move to another quantity which has a greater experimental uncertainty, namely transition pressure, and show that our approach can lead to error bars comparable to experiment. Hence, both experiment and theory can be compared on an even basis taking into account the uncertainty introduced by the scientist, both in the measuring conditions and the tuning of computational parameters.