Harmonic oscillator model, with rigid rotor approximation

At this introductory stage we can carry the comparison with the treatment of ordinary molecules further. In the first approximation these are described by the rigid rotor — harmonic oscillator model. In the next approximation an improvement is achieved by using effective operators with properties as described above. Similarly we may expect that the semirigid rotor — harmonic oscillator model for nonrigid molecules may be improved by introducing effective operators of the form,... 

The chapter starts with a brief review of thermodynamic principles as they apply to the concept of the chemical equilibrium. That section is followed by a short review of the use of statistical thermodynamics for the numerical calculation of thermodynamic equilibrium constants in terms of the chemical potential (often designated as (i). Lastly, this statistical mechanical development is applied to the calculation of isotope effects on equilibrium constants, and then extended to treat kinetic isotope effects using the transition state model. These applications will concentrate on equilibrium constants in the ideal gas phase with the molecules considered in the rigid rotor, harmonic oscillator approximation. 

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