A new method is presented, which allows an important reduction of the size of some Configuration Interaction (CI) matrices. Starting from a Complete Active Space (CAS), the numerous configurations that have a small weight in the CAS wave function are eliminated. When excited configurations (e.g., singly and doubly excited) are added to the reference space, the resulting MR-SDCI space is reduced in the same proportion as compared with the full CAS-SDCI. A set of active orbitals is chosen, but some selection of the most relevant excitations is performed because not all the possible excitations act as SDCI generators. Thanks to a new addressing technique, the computational time is drastically reduced, because the new addressing of the selected active space is as efficient as the addressing of the CAS. The presentation of the method is followed by two test calculations on the N(2) and HCCH molecules. For the N(2) the FCI results are taken as a benchmark reference. The outer valence ionization potentials of HCCH are compared to the experimental values. Both examples allow to test the accuracy of the MR-SDCI compared to that of the corresponding CAS-SDCI, despite the noticeable reduction of the CI space. The algorithm is suitable for the dressing techniques that allow for the correction of the size-extensivity error. The corrected results are also shown and discussed.
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