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Out of a freely chosen reference space (not necessarily a CAS space) all single and double exciatations are performed. The method developed [9] and later extended [10] still uses the Epstein-Nesbet scheme for selection purposes but the energy contributions from the non selected configurations are no longer summed up. Instead the MR-MP2 equations are solved within the expansion space of the non selected configurations. The MP2 energy is simply added without any weighting factor to the variational selected MRCI energy. The following figure illustrates this scheme.

To solve (11) in a direct manner $\bf\sf H_{0}^{}$ is evaluated in each iteration. $\hat{{H}}_{0}^{}$ was chosen to be an effective one particle operator with the highest contributing excitations beeing single ones. For implementation purposes the internal/external separation [11,12] is a powerful tool to neglect higher excitations efficiently. Therefore the current implementation is based on the internal/external separation and uses the same algorithms as the DIESEL-CI [1]. The solution vector $\vec{x}$ consists of the complete generated space and may therefore not necessarily fit into the main memory. This has to be taken into account for the choice of the numerical method used to solve the linear equation system. Typically a compromise between disk space consumption and iteration cycles to gain convergence must be made. It may be noted that this approach is a generalization of the CASPT2 method [13] in its N-variant [14] form because it uses the same $\hat{{H}}_{0}^{}$ operator but has no comparably restrictive requirements on the reference wave function. In the special case CASSCF orbitals are beeing used and the reference set is chosen to be the CAS space one gets the same results if no selection is done. However as this approach does not exploit the special properties of the CASSCF reference function it is less efficient in the final solution of the linear equation system because due to the missing partial diagonalization of the Fock matrix the $\hat{{H}}_{0}^{}$-matrix is less diagonal dominant.