使2-电子响应约化密度矩阵近似N-可表示的方法
Method For Making 2-Electron Response Reduced Density Matrices Approximately N-representable
摘要：
在诸如基于孪晶的方法或使用投影薛定谔方程求解的耦合团簇的方法中，直接计算2-电子约化密度矩阵（2-RDM）是不切实际的，并且人们回到基于响应理论的2-RDM。然而，来自响应理论的2-RDM不是$N$可表示的。即，响应2-RDM不对应于实际的物理$N$ -电子波函数。我们提出了一种新的算法，使这些非$N$ -可表示的2-RDM近似$N$ -可表示，即它具有正确的对称性和规范化，它满足$P$ -，$Q$ -和$G$ -条件。旁边的算法，可适用于任何2-RDM，我们还开发了一个2-RDM优化程序，专门为零的2-RDM。我们的目标是找到2-RDM与正确的属性是最接近的（在Frobenius范数的意义上）的非N-可表示的2-RDM，通过最小化的平方范数之间的差异的初始2-RDM和目标2-RDM的限制下，迹是规范化的和2-RDM，$Q$ -和$G$ -矩阵是半正定的，即它们的特征值是非负的。我们的方法适用于固定非N-可表示的2-RDM，其接近于N-可表示。通过N-可表示性优化算法，我们对初始2-RDM添加了一个小的修正，使其满足最重要的N-可表示性条件。
英文摘要：
In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not $N$-representable. That is, the response 2-RDM does not correspond to an actual physical $N$-electron wave function. We present a new algorithm for making these non-$N$-representable 2-RDMs approximately $N$-representable, i.e. it has the right symmetry and normalization and it fulfills the $P$-, $Q$- and $G$-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties that is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between the initial 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, $Q$- and $G$-matrices are positive semidefinite, i.e. their eigenvalues are non-negative. Our method is suitable for fixing non-N-respresentable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.
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