Simple techniques to predict the melting point (Tm) and boiling point (Tb) of non-hydrogen bonding rigid molecules have been developed. The compounds used include halogen, methyl, cyano, and nitro derivatives of benzene and polycyclic compounds. Melting point prediction uses additive constitutive properties e.g., molecular fragments and a non-additive non-constitutive property, molecular symmetry. Boiling point estimation employs only additive constitutive properties. It was found that symmetry affects the entropy of melting which in turn affects the melting point.