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Quantum mechanical calculations for calculating energies, vibrational wave numbers and geometries of 7- amino-4-methylcoumarin (7A4MC) have been performed by Hartree-Fock Molecular Orbital Theory (HFMOT) and Density Functional Theory (DFT) by hybrid functional B3LYP containing 6-311++G(d,p) as a basis set. Optimum values of geometrical parameters determined through HFMOT and DFT calculations are well accordance with experimental data obtained from X-ray diffraction analysis. A comprehensive interpretation of infrared spectra belong to 7A4MC is also described. Non-linear optical investigations of 7A4MC have also carried out by HFMOT and DFT through hybrid functional B3LYP with 6-311++G(d,p) as a basis set. Natural bond orbital examination of 7A4MC is also performed. [ABSTRACT FROM AUTHOR]