短程電子交換自由能

Abstract

對於一個均勻電子系統在任意密度及溫度之下，我們提出了一個足夠精準的短程電子交換自由能公式.近年來，由於高溫密度泛函理論對於熱化學以及電子結構的計算上越趨重要，然而在泛函的發展上卻顯得相對不足，以往的高溫計算利用Hartree-Fock (HF)或是局部密度近似(LDA)，然而HF無精確的相關能泛函，LDA在遠距離時會有自我作用誤差，皆無法得到足夠精準的計算值。混合泛函結合HF以及LDA可有效降低計算上的誤差但是卻無法消除自我作用誤差;長距離修正混合泛函的發展提供了一個在長距離時可消除自我作用誤差的方法，結合長程HF以及短程LDA，修正自我作用誤差可在化學反應的過渡態及電子轉移的能量上計算更精確，而本論文提出的短程電子交換自由能可提供遠距離修正混合泛函在高溫計算的需求。

We propose an analytic representation of the short-range exchange free energy for a homogeneous electron system at various temperatures and densities. This short-range exchange free energy is needed for the development of Mermin-Kohn-Sham finite temperature density functional theory (FT-DFT), which is increasingly important in electronic structure and thermochemistry. Our resulting short-range exchange free energy, based on LDA allows the range-separated hybrid functionals, such as the widely used LC hybrids to be available in FT-DFT. We also provide the theoretical calculations of heat of reactions with various temperatures and the range-separated parameter omega.