PYTHON-BASED COMPUTATIONAL ANALYSIS AND VISUALIZATION OF VIBRATIONAL–ROTATIONAL BEHAVIOR IN SELECTED DIATOMIC MOLECULES
The vibrational and rotational motions of diatomic molecules play a crucial role in understanding their structural andspectroscopic properties. In the present study, a computational approach using Python has been developed to analysevarious aspects of molecular vibrations within the harmonic and anharmonic oscillator frameworks. The potential energy variation with force constant was examined, and vibrational energies for several diatomic molecules (F–F, H–H, N–N, H–F, N–O, and C–O) were computed for different vibrational levels. The results showthat the energylevels of the anharmonic oscillator are consistently lower than those of the harmonic oscillator and that the energygap between successive levels decreases with increasing vibrational quantum number. The maximumvibrational quantum level, anharmonicity constant, and dissociation energy were also determined computationally. Furthermore, Boltzmann statistics were employed to evaluate the population distribution among vibrational and rotational energylevels at room temperature, revealing that the majority of molecules occupy the ground vibrational state. Anovel computational visualization method has been proposed to represent energy levels, wave functions, and probabilitydensities simultaneously on a single graphical scale. This integrated representation enhances the interpretationof quantum mechanical behaviour and provides an effective pedagogical tool for teaching molecular quantummechanics using modern computational techniques.
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