AI 中文总结
本研究在NESSIE框架内实现LDA-1/2的全电子有限元版本，将其应用于GW100分子基准集，获0.472 eV平均绝对误差，优于传统LDA，为分子系统提供LDA-1/2基准数据并奠定有限元基础。
AI 中文摘要
LDA-1/2方法可对半局部密度泛函理论进行有效校正，以改善电离能和带隙，但该方法在分子系统中的应用仍有限。本研究在NESSIE电子结构框架内实现了LDA-1/2的全电子有限元实现，并将其应用于GW100分子基准集合，数值精度可系统控制。自能校正通过对每个分子的中性和半电离计算显式构建，避免使用预先计算的原子校正势。实空间有限元公式化可实现离散化相关的系统收敛，并能对LDA-1/2的性能进行可控评估。对于GW100集合，该实现相对于CCSD(T)参考电离能，产生的平均绝对误差为0.472 eV，均方根误差为0.645 eV，显著优于传统LDA和先前报道的LDA-1/2的LAPW实现，同时达到与G0W0@PBE相当的精度。收敛测试表明，对于所考虑的代表性系统，三阶有限元足以达到或接近相对于高阶计算的化学精度。所得校正哈密顿量相对于LDA还改善了几个较低的价态，尽管远离HOMO时的改善变得较不系统。本研究为分子系统提供了准确的LDA-1/2基准数据，并为未来的分子GW计算建立了严格的有限元基础。
英文摘要
The LDA-1/2 method provides an efficient correction to semilocal density functional theory for improving ionization energies and band gaps, yet its application to molecular systems has remained limited. In this work, we present an all-electron finite-element implementation of LDA-1/2 within the NESSIE electronic-structure framework and apply it to the GW100 molecular benchmark set with systematically controllable numerical accuracy. The self-energy correction is constructed explicitly from neutral and half-ionized calculations for each molecule, avoiding the use of precomputed atomic correction potentials. The real-space finite-element formulation enables systematic convergence with respect to the discretization and provides a controlled assessment of LDA-1/2 performance. For the GW100 set, the present implementation yields a mean absolute error of 0.472 eV and a root-mean-square error of 0.645 eV relative to CCSD(T) reference ionization energies, substantially improving upon conventional LDA and the previously reported LAPW implementation of LDA-1/2, while achieving accuracy comparable to G0W0@PBE. Convergence tests show that third-order finite elements are sufficient to reach or approach chemical accuracy relative to higher-order calculations for the representative systems considered. The resulting corrected Hamiltonian also improves several lower lying valence states relative to LDA, although the improvement becomes less systematic away from the HOMO. This work provides accurate LDA-1/2 benchmark data for molecular systems and establishes a rigorous finite-element foundation for future molecular GW calculations.
