The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting "universal" explicitly correlated approaches that fit into the FCIQMC framework: the [2]$_{R12}$ method of Kong and Valeev [J. Chem. Phys. 135, 214105 (2011)] and the explicitly correlated canonical transcorrelation approach of Yanai and Shiozaki [J. Chem. Phys. 136, 084107 (2012)]. The former is an $extit{a posteriori}$ internally contracted perturbative approach, while the latter transforms the Hamiltonian prior to the FCIQMC simulation. These comparisons are made across the 55 molecules of the G1 standard set. We found that both methods consistently reduce the basis set incompleteness, for accurate atomization energies in small basis sets, reducing the error from 28 mE$_h$ to 3-4 mE$_h$. While many of the conclusions hold in general for any combination of multireference approaches with these methodologies, we also consider FCIQMC-specific advantages of each approach.
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机译:事实证明,全配置相互作用量子蒙特卡罗(FCIQMC)方法能够在有限轨道基集中提供电子薛定ding方程的近似精确解,而无需依赖于参考状态的展开。然而,该方法的缺点在于,基于Slater行列式的扩展,FCIQMC方法存在基集不完全性误差,该误差随所采用的单个粒子的大小而衰减得非常慢。使用显着相关的技术可以显着改善在小基础集上获得的FCIQMC结果。在这里,我们提出一项研究,评估并比较适合FCIQMC框架的两种截然不同的“通用”显式相关方法:Kong和Valeev的[2] $ _ {R12} $方法[J.化学物理135,214105(2011)]和Yanai和Shiozaki的显式相关正则互相关方法[J.化学物理136,084107(2012)]。前者是内部收缩的摄动方法,后者是在FCIQMC模拟之前转换哈密顿量的方法。这些比较是针对G1标准集的55个分子进行的。我们发现,这两种方法都能一致地减少基集的不完整性,从而在小基集中获得精确的雾化能量,从而将误差从28 mE $ _h $降低至3-4 mE $ _h $。尽管许多结论总体上适用于多参考方法与这些方法的任何组合,但我们还考虑了每种方法特定于FCIQMC的优势。
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