This invention is directed to a method of preventing or treating diseases or conditions associated with platelet aggregation. The method is also directed to a method of treating thrombosis or related disorders. The method comprises administering to a subject a pharmaceutical composition comprising an effective amount of a non-nucleotide pyrimidine-based compound, preferably a P2Y12 receptor antagonist compound, wherein said amount is effective to inhibit platelet aggregation. The compounds useful for this invention include compounds of general Formulae I and Ia-Ic, or tautomers, salts, hydrates, and solvates thereof. The present invention also provides novel compounds of Formulae I and Ia-Ic.