Spherical Harmonics The implementation of ISPHER in $CONTRL does not rely on using a spherical harmonic basis set, in fact the atomic basis remains the Cartesian Gaussians. Instead, certain MOs formed from particular combinations of the Cartesian Gaussians (for example, xx+yy+zz) are deleted from the MO space. Thus a run with ISPHER=1 will have fewer MOs than AOs. Since neither the occupied nor virtual MOs contain any admixture of xx+yy+zz, the resulting energy and wave- function is exactly equivalent to the use of a spherical harmonic basis. The log file output will contain expansions of each MO in terms of 6 d's, 10 f's, and 15 g's, and the $VEC also contains the same expansion over Cartesian Gaussians. Both the matrix in your log file and in $VEC will contain fewer MOs than AOs, the exact number of MOs used is printed in the initial guess section of the log file. It should be possible to read such $VEC groups into runs with different settings of ISPHER, should you choose to do so. The advantage of this approach is that intelligence in the generation of symmetry orbitals combined with the capability to drop linearly dependent MO combinations means that the details of ISPHER are located only in the orbital optimization code, where the variational spaces are simply reduced in size to eliminate the undesired contaminant functions. This means that none of the integral routines need be modified, as the atomic basis remains the Cartesian Gaussians. The disadvantage is that AO integral files run over the Cartesian Gaussians, and thus are not reduced in size. Of course transformed MO integrals and various computations in correlated calculations are reduced in size, since the number of MOs may be greatly reduced. Computationally, the advantages of ISPHER=1 are not limited to the reduced CPU time associated with fewer total MOs. Questions about d orbital participation as measured by Mulliken populations are cleanly addressed when the d's usage in the MOs does not contain any contamination from the s shape xx+yy+zz. Less obviously, the use of spherical harmonics frequently greatly reduces problems with linear dependency, that exhibit as poor SCF convergence.