Schweigert Igor V, Lotrich Victor F, Bartlett Rodney J
Quantum Theory Project, University of Florida, Gainesville, FL 32611, USA.
J Chem Phys. 2006 Sep 14;125(10):104108. doi: 10.1063/1.2212936.
Orbital-dependent exchange-correlation functionals are not limited by the explicit dependence on the density and present an attractive alternative to conventional functionals. With the successful implementation of the exact orbital-dependent exchange functional, the challenge lies in developing orbital-dependent approximations for the correlation functional. Ab initio many-body methods can provide such approximations. In particular, perturbation theory with the Kohn-Sham model as the reference [Görling and Levy, Phys. Rev. A 50, 196 (1994)] defines the exact correlation functional via an infinite perturbation series. The second-order term of these series gives the lowest-order approximation to the correlation functional. However, it has been suggested [Bartlett et al., J. Chem. Phys. 122, 034104 (2005)] that the Kohn-Sham Hamiltonian is not the optimal choice for the perturbation expansion and a different reference Hamiltonian may lead to an improved perturbation series and more accurate second-order approximation. Here, we demonstrate explicitly that the modified series can be used to define superior functional and potential. We present results of atomic and molecular calculations with both second-order functionals. Our results demonstrate that the modified functional offers a significantly improved description of the correlation effects as it does not suffer from convergence problems and results in energies and densities that are more accurate than those obtained with second-order Møller-Plesset perturbation theory or generalized-gradient approximation functionals.
轨道依赖的交换关联泛函不受对密度显式依赖的限制，是传统泛函颇具吸引力的替代方案。随着精确轨道依赖交换泛函的成功实现，挑战在于开发关联泛函的轨道依赖近似。从头算多体方法可以提供此类近似。特别是，以Kohn-Sham模型为参考的微扰理论[Görling和Levy，《物理评论A》50，196（1994）]通过无限微扰级数定义了精确的关联泛函。这些级数的二阶项给出了关联泛函的最低阶近似。然而，有人提出[Bartlett等人，《化学物理杂志》122，034104（2005）]，Kohn-Sham哈密顿量不是微扰展开的最佳选择，不同的参考哈密顿量可能会导致改进的微扰级数和更精确的二阶近似。在此，我们明确证明修改后的级数可用于定义更优的泛函和势。我们展示了使用两种二阶泛函进行原子和分子计算的结果。我们的结果表明，修改后的泛函对关联效应的描述有显著改进，因为它不存在收敛问题，并且得到的能量和密度比用二阶Møller-Plesset微扰理论或广义梯度近似泛函得到的更准确。
