多重态分裂的一阶自适应微扰理论
First-order symmetry-adapted perturbation theory for multiplet splittings
摘要：
我们提出了一个自适应微扰理论（SAPT）的相互作用的两个高自旋开壳层分子（由其限制的开壳层Hartree-Fock行列式描述）导致低自旋态的复杂。以前可用的SAPT形式主义，除了一些系统特定的研究少电子复合物，仅限于相互作用系统的高自旋态。因此，新的方法提供了，为第一次，一个基于SAPT的估计不同的自旋状态的复杂之间的分裂。我们已经推导并实现了负责这些分裂的最低阶SAPT项，即一阶交换能。我们表明，在SAPT中常用的所谓S2近似（忽略作为分子间重叠积分的四次或更高次幂而消失的效应）内，所有多重态的一阶交换能都是两个矩阵元素的线性组合：对角交换项决定自旋平均效应和负责状态之间分裂的{ \em自旋翻转项}。这个线性组合中的数值因子仅由Clebsch-Gordan系数决定：因此，S2近似意味着海森堡哈密顿图像，其中一个耦合强度参数决定了所有的分裂。新的方法是铸造成分子轨道和原子轨道表达式：后者使一个有效的密度拟合的实施。我们测试了新开发的形式主义的几个开壳层配合物，从双原子系统（Li+H，Mn+Mn，.）转化为非那烯基二聚体。
英文摘要：
We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S2 approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a {\em spin-flip term} responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S2 approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li+H, Mn+Mn,...) to the phenalenyl dimer.
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