During the analyzing processes of the compounds, some researchers are puzzled by the analytical signals for some TSNAs (with or without splitting peaks at various pHs and temperatures). In this work, a detailed theoretical study of structural and thermal properties of the $E/Z$ isomers of TSNAs and the corresponding protonated structures was performed using DFT methods. The calculations showed that the $E$ isomers are almost stable than $Z$ isomers, while the $Z$ isomers would be more stable when in protonation. The calculated results predicted the possibility of separation of their $E$ and $Z$ isomer forms and also showed that protonation affects the dipole moment of molecules significantly (0.1-0.5 to 0.7-2.1 Debye). The calculations agreed well with the experiments that the split-up of the HPLC signal for TSNAs into two peaks are very sensitive to the pH and temperature of the mobile-phase.