6-amino-2-mercapto-3H-pyrimidin-4-one (AMP) is a π-conjugated organic molecule extensively used as a semiconductor in many optoelectronic devices. The computational hybrid meta-generalized gradient Minnesota M06-2x, ωB97XD, and B3LYP functionals in conjunction with the correlation consistent polarized valence triplet zeta (cc-pVTZ) basis set and the moderate composite CBS-QB3 procedure were used with the aid of the Gaussian 09 program and the kinetic and statistical thermodynamical package (KiSThelP) in the temperature range 250–400 K to investigate the behavior of AMP in the gas phase, and in different polar (water, ethanol), and non-polar (dimethyl sulfoxide (DMSO), acetone)) solvents. Non-linear optical (NLO) characteristics and quantum chemical parameters were examined. Natural bond orbital analysis (NBO) was used to characterize the charge transfer of the electron density in the investigated compounds. The quality of the methods used was inspected and compared to give accurate results. The stability of AMP can be returned to the hyper conjugative interactions that leading to its nonlinear optical activity. Also, the charge delocalization was analyzed using natural bond orbital technique. The molecular electrostatic potential surfaces (MEPS) plots have been generated. The rate coefficients of tautomerization processes (kuni, in s−1) were calculated from the transition state theory (TST) and unimolecular Rice-Ramsperger-Kassel-Marcus (RRKM) methods. The results indicate comparable chemical rates obtained from TST and RRKM. In addition, positive temperature dependencies were located for all channels and a high dominance of transferring H-atom from the external N-atom to the S-atom (R3 reaction) during the applied temperature range which can return to its lower activation energy. This study is the first stone in studying AMP under different conditions such as the atmosphere, combustion conditions and as a nano catalyst.