Finite Elements and wavelets for density functional developments

对于许多电子系统，全数值解方法（有限差分（FD），有限元（FEM）和小波）现在已经超过了基本方法（LCAO， STO， GTO等）的效率（精度与计算机工作），使得非常精确的密度函数基准在相对论和非相对论上都优于10-10。它们缺乏任何重要的基依赖性，为其他解决方法提供了校准，并对重要的多体近似（Harttree-Fock, MP2，密度泛函）进行了非常详细的研究。与澳大利亚内森格里菲斯大学的J.F. Dobson合作，研究了密度泛函的有限元和小波的强大功能以及3n维Schrödinger方程应使用的直接解，用于开发和测试新的交换相关密度泛函，包括色散（范德华）贡献。

Fully numerical solution methods (finite differences (FD), finite elements (FEM) and wavelets) have surpassed by now the efficiency (accuracy vs. computer effort) of basis methods (LCAO, STO, GTO, etc.) for a number of electronic systems, enabling very accurate density functional benchmarks both relativistically and non-relativistically better than 10-10. Their lack of any significant basis dependence provides calibration for other solution methods and very detailed investigations of important many-body approximations (Harttree-Fock, MP2, denisty functionals). The very power of FEM and wavelets for density functionals and direct solutions of the 3n dimensional Schrödinger equation shall be used for the development and testing of new exchange-correlation density functionals including dispersion (Van der Waals) contributions with the group of J.F. Dobson, Griffith University, Nathan, Australia.