波函数
哈密顿量(控制论)
希尔伯特空间
子空间拓扑
全配置交互
组态交互作用
特征向量
数学
哈密尔顿矩阵
量子力学
应用数学
物理
数学分析
对称矩阵
数学优化
分子
摘要
This work develops and illustrates a new method of calculating "chemically accurate" electronic wavefunctions (and energies) via a truncated full configuration interaction (CI) procedure, which arguably circumvents the large matrix diagonalization that is the core problem of full CI and is also central to modern selective CI approaches. This is accomplished simply by following the standard/ubiquitous Davidson method in its "direct" form-wherein, in each iteration, the electronic Hamiltonian operator is applied directly in second quantization to the Ritz vector/wavefunction from the prior iteration-except that (in this work) only a small portion of the resultant expansion vector is actually even computed (through the application of only a similarly small portion of the Hamiltonian). Specifically, at each iteration of this truncated Davidson approach, the new expansion vector is taken to be twice as large as that from the prior iteration. In this manner, a small set of highly truncated expansion vectors (say 10-30) of increasing precision is incrementally constructed, forming a small subspace within which diagonalization of the Hamiltonian yields clear, consistent, and monotonically variational convergence to the approximate full CI limit. The good efficiency in which convergence to the level of chemical accuracy (1.6 mhartree) is achieved suggests, at least for the demonstrated problem sizes-Hilbert spaces of 1018 and wavefunctions of 108 determinants-that this truncated Davidson methodology can serve as a replacement of standard CI and complete-active space approaches in circumstances where only a few chemically significant digits of accuracy are required and/or meaningful in view of ever-present basis set limitations.
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