A theoretical study on the molecular polarization of thiophene and furan under the action of an electric field using Local Quantum Similarity Indexes (LQSI) was performed. This model is based on Hirshfeld partitioning of electron density within the framework of Density Functional Theory (DFT). Six local similarity indexes were used: overlap, overlap-interaction, coulomb, coulomb-interaction, Euclidian distances of overlap, and Euclidean distances of coulomb. In addition Topo-Geometrical Superposition Algorithm (TGSA) was used as a method of alignment. This method provides a straightforward procedure to solve the problem of molecular relative orientation. It provides a tool to evaluate molecular quantum similarity, enabling the study of structural systems, which differ in only one atom such as thiophene and furan (point group<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mtext>C</mml:mtext></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mtext>v</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math>) and cyclopentadienyl molecule (point group<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mtext>D</mml:mtext></mml:mrow><mml:mrow><mml:mn mathvariant="normal">5</mml:mn><mml:mtext>h</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math>). Additionally, this model can contribute to the interpretation of chemical bonds, and molecular interactions in the framework of the solvent effect theory.