Brueckner orbitals, and the density of the Brueckner reference-state, are shown to satify the same cusp condition -- involving the nuclear charges -- as natural- and Hartree--Fock-orbitals. Using the cusp condition, the density of a determinantal state can be used to determine the external potential, if the determinantal state is from either Hartee--Fock or Brueckner-orbital theory, as well as, determinant states obtained by many other formalisms that are defined by a one-body operator, if a portion of the one-body operator -- the portion not associated with the kinetic energy or external potential -- generates a well behaved function when acting on an occupied orbital. Using this relationship involving a determinant and its external potential, a variation of Reference--State One--Particle Density--Matrix Theory (physics/0308056) is formulated, where the trial wavefunctions are universal, in the Kohn-Sham sense, since they do not depend on the external potential. The resulting correlation-energy functionals, are also, universal, except for a relatively small term involving the portion of the expectation value of the external potential with the trial wavefunctions that appears beyond the first order. The same approximate energy functionals that were shown to be valid for the previous v-dependent, Reference--State One--Particle Density--Matrix Theory (physics/0308084), are shown to be valid for the current approach, except that the use of the LYP and Colle--Salvetti functional appear more natural within the current approach, since these functionals are universal ones. And since the BLYP and B3LYP functionals contain the LYP functional, these approaches are also better suited with the current approach.
Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes
在早期的工作[J. Chem. Phys. 144，064102（2016）]中，我们引入了二阶N电子价态微扰理论（t-NEVPT 2）的时间依赖性公式，其（i）具有比通常的内部收缩微扰公式更低的计算标度，并且（ii）产生完全未收缩的NEVPT 2能量。在这里，我们提出了一个组合的t-NEVPT 2与矩阵产品状态（MPS）的参考波函数（t-MPS-NEVPT 2），允许计算未收缩的动态相关能量为大的活性空间和基组，使用时间相关的密度矩阵重整化群（TD-DMRG）算法。此外，我们报告了一个低尺度的MPS为基础的实施强收缩NEVPT 2（sc-MPS-NEVPT 2），避免了计算的四粒子约简密度矩阵。我们使用这些新的方法来计算的铬二聚体的解离能和研究的低-躺在激发态的全反式多烯（C $_4$ H $_6$ C $_{24}$ H $_{26}$），将动态相关的参考波函数与多达24个活性电子和轨道。
Reference-State One-Particle Density-Matrix Theory
A density-matrix formalism is developed based on the one-particle density-matrix of a single-determinantal reference-state. The v-representable problem does not appear in the proposed method, nor the need to introduce functionals defined by a constrained search. The correlation-energy functionals are not universal; they depend on the external potential. Nevertheless, model systems can still be used to derive universal energy-functionals. In addition, the correlation-energy functionals can be partitioned into individual terms that are -- to a varying degree -- universal; yielding, for example, …
Using the local density approximation and the LYP, BLYP, and B3LYP functionals within Reference--State One--Particle Density--Matrix Theory
For closed-shell systems, the local density approximation (LDA) and the LYP, BLYP, and B3LYP functionals are shown to be compatible with reference-state one-particle density-matrix theory, where this recently introduced formalism is based on Brueckner-orbital theory and an energy functional that includes exact exchange and a non-universal correlation-energy functional. The method is demonstrated to reduce to a density functional theory when the exchange-correlation energy-functional has a simplified form, i.e., its integrand contains only the coordinates of two electron, say r1 and r2, and it …
N-electron valence state perturbation theory based on a density matrix renormalization group reference function, with applications to the chromium dimer and poly-p-phenylene vinylene oligomer
