Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
J Chem Phys. 2012 Dec 14;137(22):224113. doi: 10.1063/1.4770226.
Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the accuracy and stability of WFT-in-DFT embedding calculations. In particular, we develop spin-dependent embedding potentials in both restricted and unrestricted orbital formulations to enable WFT-in-DFT embedding for open-shell systems, and develop an orbital-occupation-freezing technique to improve the convergence of optimized effective potential calculations that arise in the evaluation of the embedding potential. The new techniques are demonstrated in applications to the van-der-Waals-bound ethylene-propylene dimer and to the hexa-aquairon(II) transition-metal cation. Calculation of the dissociation curve for the ethylene-propylene dimer reveals that WFT-in-DFT embedding reproduces full CCSD(T) energies to within 0.1 kcal/mol at all distances, eliminating errors in the dispersion interactions due to conventional exchange-correlation (XC) functionals while simultaneously avoiding errors due to subsystem partitioning across covalent bonds. Application of WFT-in-DFT embedding to the calculation of the low-spin/high-spin splitting energy in the hexaaquairon(II) cation reveals that the majority of the dependence on the DFT XC functional can be eliminated by treating only the single transition-metal atom at the WFT level; furthermore, these calculations demonstrate the substantial effects of open-shell contributions to the embedding potential, and they suggest that restricted open-shell WFT-in-DFT embedding provides better accuracy than unrestricted open-shell WFT-in-DFT embedding due to the removal of spin contamination.
密度泛函理论（DFT）嵌入为相关波函数理论（WFT）方法与电子结构的较低级别描述接口提供了一个形式上精确的框架。在这里，我们报告了提高 WFT-DFT 嵌入计算准确性和稳定性的技术。特别是，我们在受限和非受限轨道公式中开发了自旋相关的嵌入势能，以实现开壳系统的 WFT-DFT 嵌入，并开发了一种轨道占据冻结技术，以提高在嵌入势评估中出现的优化有效势计算的收敛性。新技术在范德华结合的乙烯-丙烯二聚体和六水合二价铜离子的应用中得到了验证。乙烯-丙烯二聚体的离解曲线的计算表明，WFT-DFT 嵌入在所有距离上都能将 CCSD(T) 能量精确到 0.1 kcal/mol 以内，消除了由于传统交换相关（XC）泛函而导致的色散相互作用中的误差，同时避免了由于在共价键处进行子系统划分而导致的误差。WFT-DFT 嵌入在计算六水合二价铜离子中的低自旋/高自旋分裂能的应用表明，通过仅在 WFT 级别上处理单个过渡金属原子，可以消除对 DFT XC 泛函的大部分依赖；此外，这些计算还表明了嵌入势中开壳贡献的实质性影响，并且它们表明由于消除了自旋污染，受限开壳 WFT-DFT 嵌入比非受限开壳 WFT-DFT 嵌入具有更好的准确性。
