Theoret. Chim. Acta (Berl.) 67, 263-269 (1985) THEORETICA CHIMICA ACTA 9 Springer-Verlag 1985 On the number of spin functions in the first order interaction space Wtodzistaw Duch* Max-Planck-Institute fiir Physik und Astrophysik, Institut ffir Astrophysik, Karl-Schwarzschild-Strasse 1, D-8046 Garching bei Miinchen, Federal Republic of Germany A proof is given that in a configuration interaction method the first-order interaction space contains at most only twice as many spin functions as the zeroth-order space. This allows for a dramatic reduction of the size of CI expansion. For most of the high-spin systems only two spin functions for each configuration are needed. Key words: Configuration interaction method--configuration selection--high- spin systems The concept of the Hartree-Fock interacting space, used by Bunge [1], Bender and Schaefer [2], and extended to a more general concept of the first-order interaction space (FOIS) by Liu and McLean [3], plays an important role in the selection of functions in configuration interaction (CI) expansions. The length of this expansion for most open-shell systems excludes the possibility of making high-quality calculations without a clever method of selection of only the most important configuration functions (CFs). The concept of the FOIS is well justified by an analysis of the contributions of CFs based on the Reyleigh-Schr6dinger perturbation theory [3] and is frequently used as a selection scheme. In the usual classification of the CI configuration functions first a number of reference CFs is selected, spanning the zeroth-order N-particle space and covering all dominant terms in the final expansion. The space of CFs interacting through the Hamiltonian with the zeroth-order space is called the first-order interaction space. Obviously it includes singly and doubly excted CFs relatively to reference * Permanent address: Instytut Fizyki UniwersytetuMikotaja Kopernika, ul. Grudziadzka 5, 87100 Torufi, Poland