Multi-state pair-density functional theory
Multi-state pair-density functional theory
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DOI：
10.1039/d0fd00037j
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发表时间：
2020-12-01
影响因子：
3.4
通讯作者：
Truhlar, Donald G.
中科院分区：
文献类型：
--
作者：
Bao, Jie J.;Zhou, Chen;Truhlar, Donald G.
多组态对密度泛函理论（MC-PDFT）已成功地应用于基态和激发态的计算。然而，因为它们不包括电子状态之间的相互作用，MC-PDFT计算，其中每个状态的PDFT能量分别计算可以给出一个非物理的势能面（PES）的双交叉在一个区域附近的圆锥形交叉。我们最近提出了状态相互作用对密度泛函理论（SI-PDFT）来处理近简并态，通过创建一组中间态与状态相互作用，虽然这种方法是成功的，它是不方便的，因为两个SCF计算和两套轨道是必需的，因为它把基态与激发态的不平等的立足点。在这里，我们提出了两种新的方法，称为扩展多状态PDFT（XMS-PDFT）和变分多状态PDFT（VMS-PDFT），产生的中间状态在一个平衡的方式与一组轨道。前者将Granovsky提出的中间态用于扩展的多组态准简并微扰理论（XMC-QDPT）;后者通过最大化中间态的MC-PDFT能量之和得到中间态。我们还提出了一个傅立叶级数展开，使变分优化的VMS-PDFT方法方便，我们实现了这种方法（FMS-PDFT）的传统的组态相互作用求解器和密度矩阵重整化组求解器。新的方法进行了测试，为8个系统，表现出避免两个到六个国家之间的交叉点。FMS-PDFT方法在所有测试过的情况下都是成功的（本文中的所有情况，除了O-3没有测试过），XMS-PDFT在所有八种情况下都是成功的，除了混合价的情况。由于XMS-PDFT和VMS-PDFT都比XMS-CASPT 2便宜，它们将允许在更大的系统上进行良好的相关计算，而微扰理论是负担不起的。
Multi-configuration pair-density functional theory (MC-PDFT) has previously been applied successfully to carry out ground-state and excited-state calculations. However, because they include no interaction between electronic states, MC-PDFT calculations in which each state's PDFT energy is calculated separately can give an unphysical double crossing of potential energy surfaces (PESs) in a region near a conical intersection. We have recently proposed state-interaction pair-density functional theory (SI-PDFT) to treat nearly degenerate states by creating a set of intermediate states with state interaction; although this method is successful, it is inconvenient because two SCF calculations and two sets of orbitals are required and because it puts the ground state on an unequal footing with the excited states. Here we propose two new methods, called extended-multi-state-PDFT (XMS-PDFT) and variational-multi-state-PDFT (VMS-PDFT), that generate the intermediate states in a balanced way with a single set of orbitals. The former uses the intermediate states proposed by Granovsky for extended multi-configuration quasi-degenerate perturbation theory (XMC-QDPT); the latter obtains the intermediate states by maximizing the sum of the MC-PDFT energies for the intermediate states. We also propose a Fourier series expansion to make the variational optimizations of the VMS-PDFT method convenient, and we implement this method (FMS-PDFT) both for conventional configuration-interaction solvers and for density-matrix-renormalization-group solvers. The new methods are tested for eight systems, exhibiting avoided crossings among two to six states. The FMS-PDFT method is successful for all cases for which it has been tested (all cases in this paper except O-3 for which it was not tested), and XMS-PDFT is successful for all eight cases except the mixed-valence case. Since both XMS-PDFT and VMS-PDFT are less expensive than XMS-CASPT2, they will allow well-correlated calculations on much larger systems for which perturbation theory is unaffordable.