Polycyclic aromatic hydrocarbons (PAHs) are a class of compounds consisting of more than two benzene rings fused in a linear, angular, or clustered arrangement and do not contain hetero atoms or carry subsistent. PAHs originate from various sources. They are primarily formed by incomplete combustion of carbon-containing fuels such as wood, coal, diesel, fat, or tobacco. The present study reports an investigation of the electronic structure of Pyrene by use of different model chemistries. We also made a comparison between different model chemistries. Linear relationship between the energy and Z-matrix of the structure were found. The energy diagrams vs. the number of primitive Gaussian wave functions and vs. distance matrix shows the energy variations in model chemistries HF/6-31G*, HF/6-31++G**, MP2/6-31G, MP2/6-31++G**, BLYP/6-31G, BLYP/6-31++G**, B3LYP/6-31G and B3LYP6-31-HEG**, as well. High symmetry of the Pyrene molecules makes four regions in the study of the NMR shielding tensors. The isotropic and anisotropic tensors of the Pyrene structure, calculated with different model chemistries, too. The results show that only the C and D part of the Pyrene structure are affected by the magnetic field.