Correlation of Isotope Effects with Molecular Forces. II. Triatomic Molecules

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Abstract
The theory of the relationship between the reduced partition function ratio of isotopic molecules and molecular force constants in triatomic molecules is developed through the application of finite orthogonal polynomials. Detailed calculations are presented for 13C and 18O substitution in CO2 at 500 and 1000°K, and 2H and 18O substitution in H2O at 1000 and 2000°K. The quantum correction of order j is jth order in diagonal force constant elements, but essentially linear in off‐diagonal force constant elements. Stretch‐bend interaction force constants are typically of increasing importance to the higher quantum corrections. In some cases, such as 18O substitution in water, the stretch‐bend interaction constant is an order of magnitude more important than the stretching force constant to all quantum corrections other than the simple first quantum correction. The quantum corrections are analyzed into contributions corresponding to the statistical mechanics of a single oscillating particle and coupling terms with other atoms in the molecule. The first quantum correction is always a purely statistical mechanical term. For D substitution in water, the higher‐order quantum corrections are principally statistical mechanical in origin, whereas, for 18O substitution in water, these terms are predominantly coupling terms.