第一原理计算是化学、凝聚态物理和材料科学等领域不可或缺的研究手段。材料科学中第一原理计算的核心模型是周期体系的Kohn-Sham方程。在Kohn-Sham方程求解中，数值参数的合理设置非常重要。不合理的设置可能导致数值收敛不充分的结果，从而损害后续物理分析结论的正确性。然而，现有的参数确定办法很难保证模拟结果的数值收敛程度。本项目拟在材料第一原理计算目前广泛使用的PAW方法框架下，从数学角度估计周期体系Kohn-Sham方程求解中k点采样和平面波离散带来的数值误差，并基于误差分析结果探索自动的参数调控方案，以有效降低第一原理材料计算伴随的数值精度风险，支撑高置信的武器材料状态方程建模。

First-principles calculation is an essential tool in chemistry, condensed matter physics, and materials science. The central model for first-principles calculations in materials science is the periodic Kohn-Sham equation. In solving this equation, the reasonable setting of numerical parameters is significant, or else the numerical convergence of the results cannot be ensured, making the reliability of the conclusions drawn from them untestable. Nevertheless, the present way to determine the parameters is not reliable. We propose to estimate the numerical errors from the k-point sampling and the plane wave discretization in the framework of the projector augmented-wave (PAW) method, and then explore automatic parameter tuning schemes based on the estimations. Our purpose is to decrease the risk of accuracy along with first-principles simulations, in order for a highly-reliable support for EOS (equation of state) modeling.