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Derivation of Halide Bond Lengths through Fourier Transform Infrared Spectroscopy

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  • The physical properties of hydrochloric acid and deuterium chloride were derived through the use of the harmonic oscillator and rigid rotor quantum mechanical models. By first obtaining angular momentum quantum values for HCl and DCl through Fourier Transform Infrared Spectroscopy, these two systems could be summed and processed with additional correctional terms, allowing them to more closely match real life behavior. The rotational constant, 𝐵, (10.5908, 5.4480 𝑐𝑚^-1); fundamental frequency, 𝑣!", (2885.96, 2091.06 𝑐𝑚⁻¹); vibrational correction term,𝛼, (0.3032, 0.1122𝑐𝑚⁻¹); and rotational correction term,𝐷, (5.1802E-4, 1.3776E-4𝑐𝑚⁻¹) for HCl and DCl were used to find their individual bond lengths, 𝑟, and spring constants, 𝑘. Each of the values for 𝑟 (1.2747, 1.2746 Å) and 𝑘 (516.234, 516.234 N/m) were shown to be significant based on the respective literature values (3) (𝑟 = 1.2746, 1.2746 Å; 𝑘 = 516.322, 516.347 N/m) for HCl and DCl. These data ultimately demonstrated the accuracy of the rigid rotor and harmonic oscillator models when applied to molecular systems.
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