SDS: the ‘static–dynamic–static’ framework for strongly correlated electrons

Abstract A genetic ‘static–dynamic–static’ (SDS) framework is proposed for describing strongly correlated electrons. It permits both simple and sophisticated parameterizations of many-electron wave functions. One particularly simple realization amounts to constructing and diagonalizing the Hamiltonian matrix in the same number of many-electron basis functions in the primary (static), external (dynamic) and secondary (static) subspaces of the full Hilbert space. It combines the merits of both internally and externally contracted configuration interaction as well as intermediate Hamiltonian approaches. When the Hamiltonian matrix elements between the contracted external functions, with the coefficients determined by first order perturbation, are approximated as the diagonal elements of the zeroth-order Hamiltonian $$H_0$$H0, we obtain a multi-state multi-reference second-order perturbation theory (denoted as SDS-MS-MRPT2) that scales computationally with the fifth power of the molecular size. Depending on how $$H_0$$H0 is defined, various variants of SDS-MS-MRPT2 can be obtained. For simplicity, we here choose $$H_0$$H0 as a multi-partitioned Møller–Plesset-like diagonal operator. Further combined with the string-based macroconfiguration technique, an efficient implementation of SDS-MS-MRPT2 is realized and tested for prototypical systems of variable near-degeneracies. The results reveal that SDS-MS-MRPT2 can well describe not only standard benchmark systems but also problematic systems. Taking SDS-MS-MRPT2 as a start, the accuracy may steadily be increased by relaxing the contraction of the external functions and/or iterating the diagonalization–perturbation–diagonalization procedure. As such, the SDS framework offers a very powerful scenario for handling strongly correlated systems.