密度泛函理论及其数值方法新进展

Recent Progress in Density Functional Theory and Its Numerical Methods

综述了密度泛函理论及其数值方法的最新进展。密度泛函理论的发展以寻找合适的交换相关近似为主线 ,从最初的局域密度近似、广义梯度近似到现在的非局域泛函、自相互作用修正 ,多种泛函形式的相继出现使得密度泛函理论可以提供越来越精确的计算结果。除了交换相关近似的发展 ,近年来密度泛函理论向含时理论、相对论等方面的扩展也很活跃。另外 ,在密度泛函理论体系发展的同时 ,相应的数值计算方法的发展也非常迅速。从古老的有限差分、有限元到新兴的小波分析都被用来实现密度泛函理论的数值计算。与此同时 ,线性标度的密度泛函理论算法日趋成熟 ,使得通过密度泛函理论研究诸如生物大分子之类的体系成为可能。随着密度泛函理论本身及其数值方法的发展 ,它的应用也越来越广泛 ,一些新的应用领域和研究方向不断涌现。

Recent progress in density functional theory (DFT) and its numerical methods is briefly reviewed. Finding good approximation for exchange-correlation function is one of the main targets in DFT. With the development of modem functionals, DFT leads to more and more accurate results. In addition, extensions of DFT to the time dependent case and relativistic limit are also active topics. Along with the progress in DFT itself, the development of corresponding numerical methods is also rapid. From the traditional finite difference (FD), finite element (FE) to novel wavelet bases, many techniques are used to pursue efficient and accurate DFT calculations. Meanwhile, the linear scaling algorithms of DFT are getting mature, which makes the application of DFT to large systems such as biological macro molecules become possible. All the progress leads DFT applicable to a broad range of problems. This trend is illustrated by some examples at the end of this article.