标题： 采用库仑衰减方法的双杂化密度泛函理论 显示英文标题

标题： Double hybrid density-functional theory using the Coulomb-attenuating method

摘要： 采用Coulomb衰减方法的双杂化近似（CAM-DH）在分离范围密度泛函微扰理论中被推导出来，类似于Cornaton最近的一项工作[{\it 等}Phys. Rev. A 88, 022516 (2013)]。 通过二阶恢复的能量表达式在控制Coulomb衰减的参数$\alpha$和$\beta$上是线性的。 该方法已在局域密度近似下在一个小测试集中进行了检验，这个测试集包括稀有气体和碱土金属二聚体以及具有单键、双键和三键的双原子分子。 在这个背景下，为混合CAM-B3LYP泛函优化的半经验参数$\alpha=0.19$和$\beta=0.46$并不能提供准确的相互作用能和总能量。 使用带有密度标度的半局域泛函，这在本工作中被忽略了，可能会导致不同的结论。 此时，有必要在更大的测试集上进行校准研究。 这留待以后的工作。 最后，我们提出了一种替代的CAM-DH方法，这种方法依赖于部分长程相互作用波函数的微扰展开。 在这种情况下，能量不再是$\alpha$和$\beta$的线性函数。 这方面的工作正在进行中。 显示英文摘要

摘要： A double hybrid approximation using the Coulomb-attenuating method (CAM-DH) is derived within range-separated density-functional perturbation theory, in the spirit of a recent work by Cornaton {\it et al.} [Phys. Rev. A 88, 022516 (2013)]. The energy expression recovered through second order is linear in the parameters $\alpha$ and $\beta$ that control the Coulomb attenuation. The method has been tested within the local density approximation on a small test set consisting of rare-gas and alkaline-earth-metal dimers as well as diatomics with single, double and triple bonds. In this context, the semi-empirical $\alpha=0.19$ and $\beta=0.46$ parameters, that were optimized for the hybrid CAM-B3LYP functional, do not provide accurate interaction and total energies. Using semi-local functionals with density scaling, that was neglected in this work, may lead to different conclusions. Calibration studies on a larger test set would be necessary at this point. This is left for future work. Finally, we propose as a perspective an alternative CAM-DH approach that relies on the perturbation expansion of a partially long-range interacting wavefunction. In this case the energy is not linear anymore in $\alpha$ and $\beta$. Work is in progress in this direction.