Department of Chemistry, Rice University, Houston, Texas 77005, USA.
J Chem Phys. 2011 Jul 28;135(4):044119. doi: 10.1063/1.3613706.
We explore the concept of seniority number (defined as the number of unpaired electrons in a determinant) when applied to the problem of electron correlation in atomic and molecular systems. Although seniority is a good quantum number only for certain model Hamiltonians (such as the pairing Hamiltonian), we show that it provides a useful partitioning of the electronic full configuration interaction (FCI) wave function into rapidly convergent Hilbert subspaces whose weight diminishes as its seniority number increases. The primary focus of this study is the adequate description of static correlation effects. The examples considered are the ground states of the helium, beryllium, and neon atoms, the symmetric dissociation of the N(2) and CO(2) molecules, as well as the symmetric dissociation of an H(8) hydrogen chain. It is found that the symmetry constraints that are normally placed on the spatial orbitals greatly affect the convergence rate of the FCI expansion. The energy relevance of the seniority zero sector (determinants with all paired electrons) increases dramatically if orbitals of broken spatial symmetry (as those commonly used for Hubbard Hamiltonian studies) are allowed in the wave function construction.
我们探讨了高龄数（定义为行列式中未配对电子的数量）在原子和分子系统中电子相关问题中的应用。尽管高龄数仅对于某些模型哈密顿量（如配对哈密顿量）是一个好的量子数，但我们表明，它提供了一种有用的电子完全组态相互作用（FCI）波函数的划分方法，将其划分为快速收敛的 Hilbert 子空间，其权重随高龄数的增加而减小。本研究的主要重点是对静态相关效应的充分描述。考虑的例子是氦、铍和氖原子的基态，N(2)和 CO(2)分子的对称解离，以及 H(8)氢链的对称解离。结果发现，通常施加在空间轨道上的对称约束极大地影响了 FCI 展开的收敛速度。如果允许波函数构建中使用具有破坏空间对称性的轨道（如通常用于 Hubbard 哈密顿量研究的轨道），则高龄数零部分（所有配对电子的行列式）的能量相关性会显著增加。
