A direct method to transform between expansions in the configuration state function and Slater determinant bases

A novel algorithm is introduced for the transformation of wave functions between the bases of Slater determinants (SD) and configuration state functions (CSF) in the genealogical coupling scheme. By modifying the expansion coefficients as each electron is spin-coupled, rather than performing a single many-electron transformation, the large transformation matrix that plagues previous approaches is avoided and the required number of operations is drastically reduced. As an example of the efficiency of the algorithm, the transformation for a configuration with 30 unpaired electrons and singlet spin is discussed. For this case, the 10 × 10⁶ coefficients in the CSF basis is obtained from the 150 × 10⁶ coefficients in the SD basis in 1 min, which should be compared with the seven years that the previously employed method is estimated to require