Chemistry Statistical thermo (diatomic molecule w/harmonic oscillator)

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To find the harmonic frequency of the OH radical using the C_ij matrix, one must recognize that a diatomic molecule has only one vibrational mode, simplifying the matrix to a single value, k, representing the spring constant. The harmonic frequency can then be calculated using the formula ω = √(k/m), where m is the reduced mass of the molecule. This approach stems from the classical problem of vibrations in coupled oscillators, as discussed in Feynman's Statistical Mechanics. Understanding the relationship between the spring constant and mass is crucial for determining vibrational frequencies. This method provides a straightforward way to analyze the vibrational characteristics of diatomic molecules.
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A diatomic molecule has only one vibrational mode. The ##C_{ij}## matrix becomes a single number, ##k##, the spring constant for the molecule. The harmonic frequency is given by ##\omega = \sqrt{\frac{k}{m}}##.
 
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