First principles approaches have revolutionized our ability in using computers to predict, explore, and design materials. A major advantage commonly associated with these approaches is that they are fully parameter-free. However, numerically solving the underlying equations requires to choose a set of convergence parameters. With the advent of high-throughput calculations, it becomes exceedingly important to achieve a truly parameter-free approach. Utilizing uncertainty quantification (UQ) and linear decomposition we derive a numerically highly efficient representation of the statistical and systematic error in the multidimensional space of the convergence parameters for plane wave density functional theory (DFT) calculations. Based on this formalism we implement a fully automated approach that requires as input the target precision rather than convergence parameters. The performance and robustness of the approach are shown by applying it to a large set of elements crystallizing in a cubic fcc lattice.

第一性原理方法彻底改变了我们使用计算机预测、探索和设计材料的能力。这些方法通常相关的一个主要优点是它们完全无参数。但是，对基本方程进行数值求解需要选择一组收敛参数。随着高通量计算的出现，实现真正的无参数方法变得极其重要。利用不确定性量化 （UQ） 和线性分解，我们推导出了平面波密度泛函论 （DFT） 计算的收敛参数多维空间中统计和系统误差的数值高效表示。基于这种形式，我们实现了一种完全自动化的方法，该方法需要输入目标精度而不是收敛参数。通过将该方法应用于在立方 fcc 晶格中结晶的大量元素，可以证明该方法的性能和稳健性。