The electronic and geometrical structures of fourteen polar molecules, which have sufficiently large dipole moments to form dipole-bound stationary states with an extra electron, are investigated with the Hartree-Fock (HF) method and second-order Moller-Plesset (MP2) perturbation theory. The molecules considered are as follow : formaldehyde, H2CO; propanal, CH3CH2CHO; pivalaldehyde, (CH3)(3)CCHO; butanal, CH3CH2CH2CHO; acetaldehyde, CH3CHO; 2-butanone, CH3CH2COCH3; trifluorobenzene, C7H5F3; cyclohexanone, C6H10O; acetone, CH3COCH3; cyclopentanone, C5H8O; cyclobutanone, C4H6O; methylacrylonitrile, CH2CCH3CN; acrylonitrile, CH2CHCN; acetonitrile, CH3CN. The electron affinities corresponding to the formation of the dipole-bound states of the anions are calculated. For all the molecules considered, except formaldehyde, the molecules are found to be able to support dipole-bound states. Almost direct proportionality is found between the dipole moment and the electron affinity (EA) in the series.