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首页> 外文期刊>The Journal of Chemical Physics >SparseMaps-A systematic infrastructure for reduced-scaling electronic structure methods. III. Linear-scaling multireference domain-based pair natural orbital N-electron valence perturbation theory
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SparseMaps-A systematic infrastructure for reduced-scaling electronic structure methods. III. Linear-scaling multireference domain-based pair natural orbital N-electron valence perturbation theory

机译：SparseMaps-用于缩减电子结构方法的系统基础架构。三，基于线性尺度多参考域的对自然轨道N电子价态微扰理论

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Multi-reference (MR) electronic structure methods, such as MR configuration interaction or MR perturbation theory, can provide reliable energies and properties for many molecular phenomena like bond breaking, excited states, transition states or magnetic properties of transition metal complexes and clusters. However, owing to their inherent complexity, most MR methods are still too computationally expensive for large systems. Therefore the development of more computationally attractive MR approaches is necessary to enable routine application for large-scale chemical systems. Among the state-of-the-art MR methods, second-order N-electron valence state perturbation theory (NEVPT2) is an efficient, size-consistent, and intruder-state-free method. However, there are still two important bottlenecks in practical applications of NEVPT2 to large systems: (a) the high computational cost of NEVPT2 for large molecules, even with moderate active spaces and (b) the prohibitive cost for treating large active spaces. In this work, we address problem (a) by developing a linear scaling "partially contracted" NEVPT2 method. This development uses the idea of domain-based local pair natural orbitals (DLPNOs) to form a highly efficient algorithm. As shown previously in the framework of single-reference methods, the DLPNO concept leads to an enormous reduction in computational effort while at the same time providing high accuracy (approaching 99.9% of the correlation energy), robustness, and black-box character. In the DLPNO approach, the virtual space is spanned by pair natural orbitals that are expanded in terms of projected atomic orbitals in large orbital domains, while the inactive space is spanned by localized orbitals. The active orbitals are left untouched. Our implementation features a highly efficient "electron pair prescreening" that skips the negligible inactive pairs. The surviving pairs are treated using the partially contracted NEVPT2 formalism. A detailed comparison between the partial and strong contraction schemes is made, with conclusions that discourage the strong contraction scheme as a basis for local correlation methods due to its non-invariance with respect to rotations in the inactive and external subspaces. A minimal set of conservatively chosen truncation thresholds controls the accuracy of the method. With the default thresholds, about 99.9% of the canonical partially contracted NEVPT2 correlation energy is recovered while the crossover of the computational cost with the already very efficient canonical method occurs reasonably early; in linear chain type compounds at a chain length of around 80 atoms. Calculations are reported for systems with more than 300 atoms and 5400 basis functions. (C) 2016 AIP Publishing LLC.
机译：多参考（MR）电子结构方法（例如MR配置相互作用或MR微扰理论）可以为许多分子现象（例如键断裂，激发态，过渡态或过渡金属配合物和簇的磁性）提供可靠的能量和特性。但是，由于其固有的复杂性，大多数MR方法对于大型系统而言仍然在计算上过于昂贵。因此，有必要开发更具计算吸引力的MR方法，以便能够将其常规应用到大规模化学系统中。在最新的MR方法中，二阶N电子价态扰动理论（NEVPT2）是一种高效，尺寸一致且无入侵者状态的方法。但是，在将NEVPT2应用于大型系统的实际应用中，仍然存在两个重要的瓶颈：（a）NEVPT2对于大分子的计算成本很高，即使在活动空间中等的情况下也是如此（b）处理大型活动空间的成本过高。在这项工作中，我们通过开发线性缩放的“部分收缩” NEVPT2方法来解决问题（a）。此开发使用基于域的本地对自然轨道（DLPNO）的思想来形成高效算法。如先前在单引用方法的框架中所示，DLPNO概念导致计算量的极大减少，同时提供了高精度（接近相关能量的99.9％），鲁棒性和黑盒特性。在DLPNO方法中，虚拟空间由成对的自然轨道跨越，该对自然轨道根据大轨道域中的投影原子轨道进行扩展，而非活动空间则由局部轨道跨越。活动轨道保持不变。我们的实现采用了高效的“电子对预筛选”功能，可跳过可忽略的无效对。使用部分收缩的NEVPT2形式主义对尚存的对进行处理。对部分收缩方案和强收缩方案进行了详细的比较，得出的结论是，由于其在非活动和外部子空间中的旋转不变，因此不鼓励将强收缩方案作为局部相关方法的基础。保守选择的最小截断阈值的最小集合控制方法的准确性。使用默认阈值，大约99.9％的规范化部分收缩NEVPT2相关能量得以恢复，而计算成本与已经非常有效的规范化方法的交叉发生得相当早。直链型化合物的链长约为80个原子。报道了具有300个以上原子和5400个基本函数的系统的计算结果。 （C）2016 AIP出版有限责任公司。

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