相对论关联电子结构计算中MP2冻结自然轨道的评估
Assessing MP2 frozen natural orbitals in relativistic correlated electronic structure calculations
摘要：
耦合团簇（CC）算法的计算规模与关联电子数和基组大小的关系是限制其应用的瓶颈。这对于基于2-或4-分量相对论性哈密顿量的计算尤其如此，其通常采用未收缩基组并导致大的虚拟分子轨道（VMO）空间。这个问题可以通过采用比由规范Hartree-Fock（HF）集提供的虚拟旋量更紧凑的虚拟旋量集来缓解，例如基于自然轨道（NO）的那些。在本文中，我们描述了一个模块的实现，用于生成相关波函数的NO，特别是MP2冻结自然轨道（MP2 FNO），作为我们的大规模并行架构的相对论耦合簇理论的新实现的一个组成部分[J. Pototschnig et.例如，J.化学理论计算17，5509，2021]。我们的实现是能够操纵复杂的和四元数密度矩阵，从而允许生成的Kramers限制和Kramers不受限制的MP2 FNO。此外，NOs在母原子轨道（AO）基上被重新表示，因此该代码也使得在AO基上生成CCSD自然轨道以供进一步分析成为可能。通过研究MP2 FNO在CCSD水平上对相关能和分子性质的截断误差，如核上的电场梯度（EFG），卤化氢HX（X=F-Ts）的电偶极矩和电四极矩，以及H $_2$ Y $_2$（Y=O-Se）的宇称破坏能差（PV），我们发现，MP2 FNO在整个周期表中以大致均匀的方式加速了相关能的收敛，并且，随着VMO空间被截断到全空间的一半左右，有可能获得对能量和所考虑的所有分子性质的可靠估计。
英文摘要：
The high computational scaling with the number of correlated electrons and the size of the basis set is a bottleneck which limits applications of coupled cluster (CC) algorithms. This is particularly so for calculations based on 2- or 4-component relativistic Hamiltonians, which often employ uncontracted basis sets and lead to large virtual molecular orbital (VMO) spaces. This problem may be alleviated by employing a more compact set of virtual spinors than those provided by the canonical Hartree-Fock (HF) set, such as those based on natural orbitals (NOs). In this paper we describe the implementation of a module for generating NOs for correlated wavefunctions, and in particular MP2 frozen natural orbitals (MP2FNOs), as a component of our novel implementation of relativistic coupled cluster theory for massively parallel architectures [J. Pototschnig et. al., J. Chem. Theory Comput. 17, 5509, 2021]. Our implementation is capable of manipulating both complex and quaternion density matrices, thus allowing for the generation of both Kramers-restricted and Kramers-unrestricted MP2FNOs. Furthermore, NOs are re-expressed in the parent atomic orbital (AO) basis, so that the code also makes it possible to generate CCSD natural orbitals in AO basis for further analysis. By investigating the truncation errors of MP2FNOs for both the correlation energy and molecular properties at CCSD level such as the electric field gradients at the nuclei (EFGs), electric dipole and quadrupole moments for hydrogen halides HX (X=F-Ts), and parity-violating energy differences (PV) for H$_2$Y$_2$ (Y=O-Se), we find that MP2FNOs accelerate the convergence of the correlation energy in a roughly uniform manner across the periodic table and that, with VMO spaces truncated to around half the size of the full spaces ones, it is possible to obtain reliable estimates for both energies and all molecular properties considered.
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