Filatov Michael, Martínez Todd J, Kim Kwang S
Department of Chemistry, School of Natural Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Korea.
Phys Chem Chem Phys. 2016 Aug 21;18(31):21040-50. doi: 10.1039/c6cp00236f. Epub 2016 Mar 7.
Ensemble density functional theory (DFT) furnishes a rigorous theoretical framework for describing the non-dynamic electron correlation arising from (near) degeneracy of several electronic configurations. Ensemble DFT naturally leads to fractional occupation numbers (FONs) for several Kohn-Sham (KS) orbitals, which thereby become variational parameters of the methodology. The currently available implementation of ensemble DFT in the form of the spin-restricted ensemble-referenced KS (REKS) method was originally designed for systems with only two fractionally occupied KS orbitals, which was sufficient to accurately describe dissociation of a single chemical bond or the singlet ground state of biradicaloid species. To extend applicability of the method to systems with several dissociating bonds or to polyradical species, more fractionally occupied orbitals must be included in the ensemble description. Here we investigate a possibility of developing the extended REKS methodology with the help of the generalized valence bond (GVB) wavefunction theory. The use of GVB enables one to derive a simple and physically transparent energy expression depending explicitly on the FONs of several KS orbitals. In this way, a version of the REKS method with four electrons in four fractionally occupied orbitals is derived and its accuracy in the calculation of various types of strongly correlated molecules is investigated. We propose a possible scheme to ameliorate the partial size-inconsistency that results from perfect spin-pairing. We conjecture that perfect pairing natural orbital (NO) functionals of reduced density matrix functional theory (RDMFT) should also display partial size-inconsistency.
系综密度泛函理论(DFT)为描述由几种电子构型的(近)简并产生的非动态电子关联提供了一个严格的理论框架。系综DFT自然地导致了几个Kohn-Sham(KS)轨道的分数占据数(FONs),因此这些轨道成为该方法的变分参数。目前以自旋限制系综参考KS(REKS)方法形式存在的系综DFT实现最初是为仅具有两个分数占据KS轨道的系统设计的,这足以准确描述单个化学键的解离或双自由基类物种的单重基态。为了将该方法的适用性扩展到具有多个解离键的系统或多自由基物种,系综描述中必须包含更多分数占据的轨道。在这里,我们研究借助广义价键(GVB)波函数理论开发扩展REKS方法的可能性。GVB的使用使人们能够导出一个简单且物理上透明的能量表达式,该表达式明确依赖于几个KS轨道的FONs。通过这种方式,我们推导了一种在四个分数占据轨道中有四个电子的REKS方法版本,并研究了其在计算各种类型强相关分子时的准确性。我们提出了一个可能的方案来改善由完美自旋配对导致的部分尺寸不一致性。我们推测,约化密度矩阵泛函理论(RDMFT)的完美配对自然轨道(NO)泛函也应表现出部分尺寸不一致性。