Peng Degao, van Aggelen Helen, Yang Yang, Yang Weitao
Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.
J Chem Phys. 2014 May 14;140(18):18A522. doi: 10.1063/1.4867540.
Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.
粒子-粒子随机相位近似（pp-RPA）的最新进展拓宽了对基态关联能[H. 范阿格伦、杨阳和杨伟，《物理评论A》88，030501（2013）；杨阳、H. 范阿格伦、S. N. 施泰因曼、彭丹和杨伟，《化学物理杂志》139，174110（2013）；彭丹、S. N. 施泰因曼、H. 范阿格伦和杨伟，《化学物理杂志》139，104112（2013）]以及N±2激发能[杨阳、H. 范阿格伦和杨伟，《化学物理杂志》139，224105（2013）]的认识。到目前为止，哈特里-福克和近似密度泛函轨道已被用于评估pp-RPA方程。在本文中，为了进一步探索依赖于配对矩阵的泛函的基本原理及其潜在用途，我们提出了具有绝热和频率依赖核的含配对场的线性响应含时密度泛函理论。该理论与超导体的密度泛函理论和含时密度泛函理论相关，但出于我们的目的应用于正常非超导系统。由于对于含时系统，配对矩阵和配对场之间缺乏一一映射的证明，线性响应理论是基于配对矩阵的可表示性假设建立的。线性响应理论证明了在pp-RPA方程中使用近似密度泛函的合理性。这项工作为未来密度泛函的发展奠定了基础，以增强对基态关联能和N±2激发能的描述。
