The structure and stability of pyrite (100), (210), (110), and (111) surfaces in different sulfur conditions were studied in the framework of GGA(PBE) + U implementations of density functional calculations. The Hubbard U correction was found to be a critical parameter in density functional theory (DFT) calculations to describe pyrite surfaces. With the U correction, the surface energy order for stoichiometric pyrite surfaces is (100) < (210) < (110) < (111), which is different with previous knowledge from conventional DFT and classical force field calculations, but consistent with broken bonds number and shape distribution in natural and synthetic systems in different sulfur conditions. Within the considered surfaces, the stoichiometric (100)-S and non-stoichiometric (111)-3S are the most stable under both S-lean and S-rich conditions, respectively. For relative stable surfaces in different environment, (100)-Fe and (100)-2S reconstruct, but (111)-Fe and (111)-3S show no relaxations while (100)-S, (210)-Fe′, and (210)-2S′ show relaxations to certain degree. Electron transfer from surface Fe to S atom on pyrite during relaxation and reconstruction, forming exemplary surface configuration and chemical composition. These findings reveal the nature of pyrite surfaces in various sulfur conditions, proving fundamental not only for surface-related applications but also for geological indicators of pyrite formation conditions.

在密度泛函计算的GGA（PBE）+ U实现的框架下，研究了在不同硫条件下黄铁矿（100），（210），（110）和（111）表面的结构和稳定性 。发现哈伯德U校正是描述黄铁矿表面的密度泛函理论（DFT）计算中的关键参数。与U校正后，化学计量黄铁矿表面的表面能阶为（100）<（210）<（110）<（111），这与传统DFT和经典力场计算的先前知识有所不同，但与断裂键的数量和形状一致在不同硫条件下在天然和合成系统中的分布。在考虑的表面内，化学计量的（100）-S和非化学计量的（111）-3S分别在贫S和富S条件下最稳定。对于在不同环境中相对稳定的表面，（100）-Fe和（100）-2S进行了重构，但是（111）-Fe和（111）-3S没有显示出弛豫，而（100）-S，（210）-Fe'， （210）-2S'显示出一定程度的弛豫。在弛豫和重构过程中，电子从表面铁转移到黄铁矿上的S原子，形成示例性的表面构型和化学组成。这些发现揭示了在各种硫条件下黄铁矿表面的性质，不仅证明了与表面相关的应用的基础，而且还证明了黄铁矿形成条件的地质指示。