Developing a computational method that is both affordable and accurate for transition-metal chemistry is a major challenge. The bond dissociation energies and the potential energy curves are two important targets for theoretical prediction. Here, we investigate the performance of multiconfiguration pair-density functional theory (MC-PDFT) based on wave functions calculated by the complete-active-space (CAS) and generalized active space (GAS) self-consistent-field (SCF) methods for three transition-metal diatomics (TiC, TiSi, and WCl) for which accurate bond energies are available from recent experiments. We compare the results to those obtained by CAS second-order perturbation theory (CASPT2) and Kohn–Sham DFT (KS-DFT). We use six systematic methods to choose the active spaces: (1) we put the bonding orbitals, antibonding orbitals, and singly occupied nonbonding orbitals into the active space in the first method; (2) we also put s and p valence orbitals into the active space; we tried two levels of correlated participating orbitals (CPO) active spaces: (3) nominal CPO (nom-CPO) and (4) extended CPO (ext-CPO); and we used (5) the separated-pair (SP) approximation and (6) a new method presented here called extended separate pairs (ESP) approximation to divide the nom-CPO active space into subspaces. Schemes 1–4 are carried out within the CAS framework, and schemes 5 and 6 are carried out in the GAS framework to eliminate deadwood configurations. For TiC and TiSi, we used all six kinds of active spaces. For WCl, we used three active spaces (nom-CPO, SP, and ESP). We found that MC-PDFT performs better than both CASPT2 and KS-DFT. We also found that the SP (for TiSi) and ESP (for TiC and WCl) approximations are particularly appealing because they make the potential curves smoother and significantly decrease the computational cost of CASSCF calculations. Furthermore, ESP-PDFT can be as accurate as CAS-PDFT.

中文翻译：

---

过渡金属势能曲线的扩展分离对近似

开发一种既经济又准确的过渡金属化学计算方法是一项重大挑战。键解离能和势能曲线是理论预测的两个重要目标。在这里，我们研究基于完全活动空间（CAS）和广义活动空间（GAS）自洽场（SCF）方法计算的波动函数的多配置对密度泛函理论（MC-PDFT）的性能，三种过渡金属硅原子（TiC，TiSi和WCl）可从最近的实验中获得准确的键能。我们将结果与通过CAS二阶微扰理论（CASPT2）和Kohn-Sham DFT（KS-DFT）获得的结果进行比较。我们使用六种系统方法来选择活动空间：（1）放置键合轨道，反键合轨道，在第一种方法中，将单个未键合轨道单独占据到活动空间中；（2）我们还将s和p价轨道放入活动空间；我们尝试了两个级别的相关参与轨道（CPO）活动空间：（3）名义CPO（nom-CPO）和（4）扩展CPO（ext-CPO）；我们使用（5）分离对（SP）近似和（6）这里介绍的一种新方法称为扩展分离对（ESP）近似将nom-CPO活动空间划分为子空间。方案1-4在CAS框架内进行，方案5和6在GAS框架内进行，以消除枯木结构。对于TiC和TiSi，我们使用了所有六种有源空间。对于WCl，我们使用了三个活动空间（nom-CPO，SP和ESP）。我们发现MC-PDFT的性能优于CASPT2和KS-DFT。我们还发现，SP（对于TiSi）和ESP（对于TiC和WCl）近似值特别有吸引力，因为它们使电势曲线更平滑并且显着降低了CASSCF计算的计算成本。此外，ESP-PDFT可以与CAS-PDFT一样精确。