强关联电子系统的粒子-空穴与粒子-粒子理论的对偶性
Duality of particle-hole and particle-particle theories for strongly correlated electronic systems
AI总结：
针对多参考体系电子关联问题，本文提出基于二阶粒子-空穴（ph）和粒子-粒子（pp）理论的新方法，利用对偶性结合二者避免重复计算，在中强关联体系基态、激发态及双自由基能隙计算中精度优于单独方法及MRPT2。
摘要：
我们提出一种针对多参考体系电子关联的新方法，该方法基于二阶粒子-空穴（ph）和粒子-粒子（pp）理论，在多参考波函数的随机相位近似（RPA）框架下发展而来。我们证明了ph和pp图像中关联能贡献之间存在形式上的对应关系（对偶性），这使得我们能够通过严格结合pp和ph项来描述关联能，避免关联的重复计算。我们将多参考ph、pp及组合关联方法应用于中强关联体系的基态和激发态，并与多参考二阶微扰方法（MRPT2）进行比较。结果表明，pp近似无法描述多键解离过程；而ph-pp组合方法整体优于单独的ph和pp方法，其基态和单重激发能的精度与二阶微扰理论相当，且对双自由基的单重-三重态能隙的精度显著更高。考虑到该方法仅依赖单体和二体密度矩阵，而MRPT2通常需要四体密度矩阵，这一结果令人印象深刻。
英文摘要：
We propose a novel approach to electron correlation for multireference systems. It is based on particle-hole (ph) and particle-particle (pp) theories in the second-order, developed in the random phase approximation (RPA) framework for multireference wavefunctions. We show a formal correspondence (duality), between contributions to the correlation energy in the ph and pp pictures. It allows us to describe correlation energy by rigorously combining pp and ph terms, avoiding correlation double counting. The multireference ph, pp, and the combined correlation methods are applied to ground and excited states of systems in the intermediate and strong correlation regimes and compared with the multireference second-order perturbation method (MRPT2). It is shown that the pp approximation fails to describe dissociation of multiple bonds. The ph-pp combined method is overall superior to both ph and pp alone. It parallels good accuracy of the second-order perturbation theory for ground states and singlet excitation energies. For the singlet-triplet gaps of biradicals its accuracy is significantly better. This is impressive, taking into account that it relies only on one- and two-body density matrices, while MRPT2 methods typically require density matrices up to the four-body.
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