The internal coordinate Morse oscillator as a means to simplify the anharmonicity problem in the thermodynamics of systems of polyatomic molecules

Two postulates simplify the evaluation and algebraic complexity of the expression for the anharmonic correction to the ground rotational–vibrational energy of a polyatomic molecule. The two postulates are: (1) anharmonicity of vibration is associated with bond stretching coordinates only; all other internal coordinates can be represented by harmonic potentials; (2) bonds vibrate according to a Morse potential. The result is the replacement of tedious computer calculations by a 'back of an envelope' type of computation. Relationships between anharmonic corrections to the ground state vibrational energies of isotopically different molecules are derived. Good agreement with exact results is obtained. Quantitative and qualitative applications are given.