Vol. 7, Issue 2, Part C (2025)

In this research, the potential energy and vibrational frequencies of the linear hydrogen cyanide (HCN) molecule were studied and calculated using semi-empirical quantum programs via the MNDO-PM3 method. The geometric structure of the studied molecule was determined through initial and final matrices containing bond lengths, bond angles, and the atomic charges of each atom in the molecule. The potential energy curve of the molecule was plotted by varying the bond lengths of (H-C) and (C≡N), and corresponding total energy values were obtained. From this, the total energy was calculated as (-302.902 eV) and (-301.52 eV) for each bond respectively, along with the equilibrium bond distances of (1.09 Å) and (1.158 Å).
Also, the values of the molecular orbital energies were computed, the highest occupied molecular orbital (EHOMO), the lowest unoccupied molecular orbital (ELUMO), and the energy gap (Egap), the latter being found to be 14.03 eV. The vibrational frequencies had also been obtained at the equilibrium geometry. Further, thermal characteristics were calculated at varying temperatures between 100 0 K and 300 0 K and plots of each characteristic versus temperature were drawn. The findings are in good agreement with a number of prior experimental studies.