The Intermediate Hamiltonian CC Method

The concept of the intermediate Hamiltonian has been proposed by MaWeu et al. [39] in the framework of degenerate perturbation theory. The P space is partitioned into the main Pm subspace, which includes all the states of interest, and the intermediate P, subspace, serving as a buffer between Pm and the rest of the functional space Q. The corresponding operators satisfy the equations 

The other eigenvalues, which correspond to states 4, ) with the largest components in P,-, may be more or less accurate. This leads to some freedom in defining the relevant eigenfunctions and eigenvalues, and, therefore, in the evaluation of problematic QSPi matrix elements. To control this freedom and make the approach more general and flexible, we also use the partitioning 

Partitioning the P and Q projectors of the FSCC equation (2.7) into the main and intermediate parts by formulas (2.9,2.12) yields four coupled CC equations. 

Only the last of these can cause convergence problems. Successful replacement of this equation by another, based on physical considerations, is the central point of the IH method. The new equation to be used instead of equation 2.16 will be called the IH condition (IHC). Ideally, it should satisfy the following demands  

Subject to these demands, the IHC should be as close to equation 2.16 as possible. 

---