距离分离系综密度泛函理论中线性内插外推方法的结合
Combining linear interpolation with extrapolation methods in range-separated ensemble density-functional theory
摘要：
最近提出的线性插值方法（LIM）[Senjean等人，Phys.Rev.A92，012518（2015）]，其使得能够在距离分离的系综密度泛函近似中计算与重量无关的激发能，其中Savin [J.Chem.Phys.140，18A509（2014）]的外推方案在这项工作中呈现。结果表明，LIM激发能随距离分离参数μ的倒数呈二次方变化，当后者较大时。因此，通常用于长程相互作用能的外推方案可以直接适用于LIM。这种外推的LIM（ELIM）已在由He，Be，H2和HeH+组成的小测试集上进行了测试。相对准确的结果已获得的第一单重态激发能与典型的mu=0.4的值。外推后LIM的改进是显著的，特别是对于拉伸H2分子中的双激发2^1 σ +g态。H2中的三态系综计算也表明ELIM不一定提高相对激发能，即使外推后单个激发能更准确。最后，提出了一种替代的短程系综交换相关能量的分解，以纠正鬼相互作用的错误，在多行列式距离分离的系综密度泛函理论计算。目前正在执行和校准这一计划。
英文摘要：
The combination of a recently proposed linear interpolation method (LIM) [Senjean et al., Phys. Rev. A 92, 012518 (2015)], which enables the calculation of weight-independent excitation energies in range-separated ensemble density-functional approximations, with the extrapolation scheme of Savin [J. Chem. Phys. 140, 18A509 (2014)] is presented in this work. It is shown that LIM excitation energies vary quadratically with the inverse of the range-separation parameter mu when the latter is large. As a result, the extrapolation scheme, which is usually applied to long-range interacting energies, can be adapted straightforwardly to LIM. This extrapolated LIM (ELIM) has been tested on a small test set consisting of He, Be, H2 and HeH+. Relatively accurate results have been obtained for the first singlet excitation energies with the typical mu=0.4 value. The improvement of LIM after extrapolation is remarkable, in particular for the doubly-excited 2^1Sigma+g state in the stretched H2 molecule. Three-state ensemble calculations in H2 also show that ELIM does not necessarily improves relative excitation energies, even though individual excitation energies are more accurate after extrapolation. Finally, an alternative decomposition of the short-range ensemble exchange-correlation energy is proposed in order to correct for ghost-interaction errors in multideterminant range-separated ensemble density-functional theory calculations. The implementation and calibration of such a scheme is currently in progress.
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