Kooi Derk P, Weckman Timo, Gori-Giorgi Paola
Department of Chemistry & Pharmaceutical Sciences and Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
J Chem Theory Comput. 2021 Apr 13;17(4):2283-2293. doi: 10.1021/acs.jctc.1c00102. Epub 2021 Mar 10.
The "fixed diagonal matrices" (FDM) dispersion formalism [Kooi, D. P.; et al. 2019, 10, 1537] is based on a supramolecular wave function constrained to leave the diagonal of the many-body density matrix of each monomer unchanged, reducing dispersion to a balance between kinetic energy and monomer-monomer interaction. The corresponding variational optimization leads to expressions for the dispersion energy in terms of the ground-state pair densities of the isolated monomers only, providing a framework to build new approximations without the need for polarizabilities or virtual orbitals. Despite the underlying microscopic real space mechanism being incorrect, as in the exact case there is density relaxation, the formalism has been shown to give extremely accurate (or even exact) dispersion coefficients for H and He. The question we answer in this work is how accurate the FDM expressions can be for isotropic and anisotropic dispersion coefficients when monomer pair densities are used from different levels of theory, namely Hartree-Fock, MP2, and CCSD. For closed-shell systems, FDM with CCSD monomer pair densities yield a mean average percent error for isotropic dispersion coefficients of about 7% and a maximum absolute error within 18%, with a similar accuracy for anisotropies. The performance for open-shell systems is less satisfactory, with CCSD pair densities performing sometimes worse than Hartree-Fock or MP2. In the present implementation, the computational cost on top of the monomer's ground-state calculations is (). The results show little sensitivity to the basis set used in the monomer's calculations.
“固定对角矩阵”（FDM）色散形式理论[Kooi, D. P.; 等人，2019, 10, 1537]基于一种超分子波函数，该波函数被约束为使每个单体的多体密度矩阵的对角线保持不变，从而将色散简化为动能与单体 - 单体相互作用之间的平衡。相应的变分优化仅根据孤立单体的基态对密度得出色散能的表达式，提供了一个无需极化率或虚拟轨道即可构建新近似方法的框架。尽管其潜在的微观实空间机制是不正确的，因为在精确情况下存在密度弛豫，但该形式理论已被证明能给出氢和氦极其精确（甚至精确）的色散系数。我们在这项工作中要回答的问题是，当使用来自不同理论水平（即哈特里 - 福克、MP2和CCSD）的单体对密度时，FDM表达式对于各向同性和各向异性色散系数的精确程度如何。对于闭壳层系统，使用CCSD单体对密度的FDM给出的各向同性色散系数的平均平均百分比误差约为7%，最大绝对误差在18%以内，各向异性的精度类似。开壳层系统的性能不太令人满意，CCSD对密度有时比哈特里 - 福克或MP2表现更差。在当前实现中，在单体基态计算之上的计算成本为（）。结果表明对单体计算中使用的基组几乎不敏感。
