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We have studied the Xα -SCF problem with an atoms in molecules approach. LCAO-molecular orbitals are used and the molecular charge and exchange densities are built up from atomic contributions. We have applied our method to CH3F with subsequent comparison to ab initio calculations. The Xα -SCF dipole moment of CH3F is 1.76 D compared with an experimental value of 1.79 D. We also give calculations of TCNQ and TTF with comparisons to recent Xα calculations using the overlapping sphere modification of a muffin-tin potential. Quadrupole moments for TCNQ and TTF have also been determined. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.