Multistate Complete-Active-Space Second-Order Perturbation Theory Based on Density Matrix Renormalization Group Reference States

We present the development of the multistate multireference second-order perturbation theory (CASPT2) with multiroot references, which are described using the density matrix renormalization group (DMRG) method to handle a large active space. The multistate first-order wave functions are expanded into the internally contracted (IC) basis of the single-state single-reference (SS-SR) scheme, which is shown to be the most feasible variant to use DMRG references. The feasibility of the SS-SR scheme comes from two factors: first, it formally does not require the fourth-order transition reduced density matrix (TRDM) and second, the computational complexity scales linearly with the number of the reference states. The extended multistate (XMS) treatment is further incorporated, giving suited treatment of the zeroth-order Hamiltonian despite the fact that the SS-SR based IC basis is not invariant with respect to the XMS rotation. In addition, the state-specific fourth-order reduced density matrix (RDM) is eliminated in an approximate fashion using the cumulant reconstruction formula, as also done in the previous state-specific DMRG-cu(4)-CASPT2 approach. The resultant method, referred to as DMRG-cu(4)-XMS-CASPT2, uses the RDMs and TRDMs of up to third-order provided by the DMRG calculation. The multistate potential energy curves of the photoisomerization of diarylethene derivatives with CAS­(26e,24o) are presented to illustrate the applicability of our theoretical approach.本工作报道了基于多根参考态的多态多参考二级微扰理论（CASPT2）的发展，该方法采用密度矩阵重整化群（DMRG）方法描述参考态以处理大活性空间。多态一阶波函数被展开为单态单参考（SS-SR）框架下的内收缩（IC）基，该框架被证明是适配DMRG参考态的最可行方案。该SS-SR框架的可行性源于两点：其一，形式上无需四阶跃迁约化密度矩阵（TRDM）；其二，计算复杂度随参考态数目呈线性缩放。进一步引入扩展多态（XMS）处理，尽管基于SS-SR的IC基不满足XMS旋转不变性，但该处理仍能对零级哈密顿量实现适配性处理。此外，采用近似方式通过累积量重构公式消去了态特异性四阶约化密度矩阵（RDM），这与此前的态特异性DMRG-cu(4)-CASPT2方法一致。所得到的方法被命名为DMRG-cu(4)-XMS-CASPT2，其仅需DMRG计算提供的至多三阶约化密度矩阵与跃迁约化密度矩阵。本文还给出了具有CAS(26e,24o)活性空间的二芳基乙烯衍生物光异构化过程的多态势能曲线，以展示该理论方法的适用性。