周期性分子系统中关联驱动现象的变分双电子约化密度矩阵理论
Correlation-Driven Phenomena in Periodic Molecular Systems from Variational Two-electron Reduced Density Matrix Theory
摘要：
分子周期系统中的相关驱动现象在计算上预测是具有挑战性的，不仅因为这样的系统是周期性无限的，而且因为它们通常是强相关的。本文推广了变分双电子约化密度矩阵（2-RDM）理论来计算强关联周期系统的能量和性质。根据必要的$N$ -可表示性条件直接计算晶胞的2-RDM，使得晶胞2-RDM表示至少一个$N$ -电子密度矩阵。两个典型的，但非平凡的系统，周期金属氢链和周期并苯，被视为演示的方法。我们发现，虽然单参考相关理论没有捕捉到这些分子系统中的强（静态）相关效应，周期变分2-RDM理论预测莫特金属到绝缘体的过渡中的氢链和长度依赖的polyradical形成并苯。对于这两个氢链和并苯的周期性计算与以前的非周期性计算的结果显示出显着的变化的能量和增加的电子相关的周期性边界条件进行了比较。2-RDM理论，它允许更大的活性空间比传统的可能，适用于研究一般周期性分子固体和材料中的相关驱动的现象。
英文摘要：
Correlation-driven phenomena in molecular periodic systems are challenging to predict computationally not only because such systems are periodically infinite but also because they are typically strongly correlated. Here we generalize the variational two-electron reduced density matrix (2-RDM) theory to compute the energies and properties of strongly correlated periodic systems. The 2-RDM of the unit cell is directly computed subject to necessary $N$-representability conditions such that the unit-cell 2-RDM represents at least one $N$-electron density matrix. Two canonical but non-trivial systems, periodic metallic hydrogen chains and periodic acenes, are treated to demonstrate the methodology. We show that, while single-reference correlation theories do not capture the strong (static) correlation effects in either of these molecular systems, the periodic variational 2-RDM theory predicts the Mott metal-to-insulator transition in the hydrogen chains and the length-dependent polyradical formation in acenes. For both hydrogen chains and acenes the periodic calculations are compared with previous non-periodic calculations with the results showing a significant change in energies and increase in the electron correlation from the periodic boundary conditions. The 2-RDM theory, which allows for much larger active spaces than are traditionally possible, is applicable to studying correlation-driven phenomena in general periodic molecular solids and materials.
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