论文标题
截短的戴维森方法，用于有效地“化学准确”计算完整构型相互作用波函数，而没有任何大型基质对角线化
A truncated Davidson method for the efficient "chemically accurate" calculation of full configuration interaction wavefunctions without any large matrix diagonalization
论文作者
论文摘要
这项工作开发并说明了一种通过截短的完整配置相互作用（CI）程序来计算“化学精确”电子波函数（和能量）的新方法，该过程可以说，该程序可以说明大型基质对角色是全CI的核心问题，并且也是现代选择的CI方法的中心。这仅通过按照其“直接”形式遵循标准/普遍存在的戴维森方法来完成 - 其中，在每种迭代中，电子哈密顿量运算符直接用于先前迭代中的ritz矢量/波函数二量化，但实际上仅计算出了一小部分扩展矢量的范围（在这项工作中（在这项工作中）仅计算出的一小部分。具体而言，在这种截断的戴维森方法的每次迭代中，新扩展向量的大小是先前迭代的两倍。以这种方式，一组高度截断的膨胀向量（例如10--30）的精度逐渐构建是逐渐构造的，形成了一个小的子空间，在该子空间中，汉密尔顿的对角线化产生了清晰，一致且单调的变异收敛到近似CI的限制。达到与化学准确性水平（1.6 mhartree）的良好效率提出了建议，至少对于所证明的问题尺寸 - $ 10^{18} $ $ 10^{18} $的希尔伯特空间和$ 10^8 $ decterations的波浪函数 - 这种截然不同的戴维森方法只能用来替代标准的ci和Cassific of Space（Case），即替代标准的动态（Cass）（Cass），即Cassixific（Case）的替代品（鉴于存在的基础设置限制，需要准确性和/或有意义。
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 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 $10^{18}$ and wavefunctions of $10^8$ determinants -- that this truncated Davidson methodology can serve as a replacement of standard CI and complete-active space (CAS) 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.
