Computer aided molecular design (CAMD) has attracted much attention in the past 30 years. The generation of a candidate molecular structure satisfying a set of structural constraints is an important part of such a problem. However, the commonly used structural constraints proposed by Odele and Macchietto [Odele, O.; Macchietto, S. Computer Aided Molecular Design: A Novel Method for Optimal Solvent Selection. Fluid Phase Equilib. 1993, 82, 47], cannot provide sufficient and necessary conditions for generating cyclic molecules. In this paper, the sufficient and necessary conditions for molecular generation were presented. According to these conditions, some modifications of the conventional constraints were made, and mathematical proofs demonstrated that the modified constraints can perfectly generate structurally feasible molecules with no more than two rings. Moreover, some new constraints were proposed to help generate feasible aromatic molecules with less than two rings. Finally, several cases were presented to validate the correctness and applicability of the proposed modifications via comparing the results of the CAMD problems using the constraints before and after modification, and the new constraints were applied to design solvents for liquid-liquid extraction. It is shown that the modifications presented in this paper can improve the reliability of results of CAMD, and additionally, the conditions of molecular generation proposed in this paper can be easily used to derive structural constraints for any type of target molecules.