密度矩阵泛函理论及其计算方法  

Density-matrix Functional Theory and Its Computational Method

作　　者：IRIMIA Marinela 王坚[2] IRIMIA Marinela;WANG Jian(International School,Huzhou University,Huzhou 313000,China;School of Science,Huzhou University,Huzhou 313000,China)

机构地区：[1]湖州师范学院国际学院,浙江湖州313000 [2]湖州师范学院理学院,浙江湖州313000

出　　处：《湖州师范学院学报》2024年第2期14-20,共7页Journal of Huzhou University

基　　金：浙江省自然科学基金项目(Y23A040010)。

摘　　要：随着密度泛函理论的普及,发明人Kohn于1998年获得诺贝尔化学奖.在密度泛函理论中,轨道占有数只取1或者0.Gilbert于1975年提出密度矩阵泛函理论,在这一理论方法中,轨道占有数除了1和0之外,还可以取0至1之间的分数.从形式上看,这一理论推广了密度泛函理论.然而,Gilbert发现当占有数为分数时,轨道能级都是简并的,这与实验观察到的能级结构不符.因为能级简并,无法像密度泛函理论那样获得真正的轨道的本征值方程,计算只能依靠非线性优化方法,计算效率很低.这个近半个世纪的难题,最近被我们攻克.我们用信息熵函数提取密度矩阵泛函理论的关联能,由此获得轨道的自洽场本征值方程,实现密度矩阵泛函理论方法的高效计算.With the popularity of density functional theory,the inventor Kohn won the Nobel prize in chemistry in 1998.In the density functional theory,the orbital occupation numbers are restricted to be 1 or 0.In 1975,Gilbert proposed density-matrix functional theory,in which the occupation numbers can take additional fractional numbers between 0 and 1.Therefore,it can be regarded as a generalization of density functional theory.However,Gilbert found that the orbital energies were all degenerate for orbitals with fractional occupation numbers,which contradicts with the energy structure observed in experiments.Because of the degeneracy,there was no real eigenvalue equation for the orbitals in density-matrix functional theory,only a non-linear optimisation method could be used in the calculation,which was very inefficient.The nearly half-a-century problem was solved by us recently.After employing the information entropy to extract the correlation energy in density-matrix functional theory,we obtain the self-consistent field eigenvalue equation for the orbitals,so that efficient computation is realized within the density-matrix functional theory.

关 键 词：密度矩阵泛函理论 信息熵 电子关联 

分 类 号：O413[理学—理论物理]