ABSTRACT
For diatomic molecules, we are able to obtain a much broader range of information from experimental data than is possible for larger molecules. In addition to equilibrium structures, we can often determine an accurate bond dissociation energy, an accurate potential curve for the whole potential well, and sometimes also the Born-Oppenheimer breakdown (BOB) radial strength functions, which dene the small differences between the electronic and centrifugal potential energy functions for different isotopologues of a given species. Such results allow us to make realistic
6.1 Quantum Mechanics of Vibration and Rotation ........................................... 160 6.2 Semiclassical Methods .................................................................................. 164
6.2.1 The Semiclassical Quantization Condition ...................................... 164 6.2.2 The Rydberg-Klein-Rees Inversion Procedure ............................... 168 6.2.3 Near-Dissociation Theory ................................................................. 174 6.2.4 Conclusions Regarding Semiclassical Methods ............................... 183
6.3 Quantum-Mechanical Direct-Potential-Fit Methods .................................... 184 6.3.1 Overview and Background ............................................................... 184 6.3.2 Potential Function Forms .................................................................. 185
6.3.2.1 Polynomial Potential Function Forms ............................... 186 6.3.2.2 The Expanded Morse Oscillator Potential Form and the
Importance of the Denition of the Expansion Variable .... 188 6.3.2.3 The Morse/Long-Range (MLR) Potential Form ............... 190 6.3.2.4 The Spline-Pointwise Potential Form ................................ 193
6.3.3 Initial Trial Parameters for Direct Potential Fits .............................. 194 6.4 Born-Oppenheimer Breakdown Effects ...................................................... 195 6.5 Conclusion .................................................................................................... 198 Appendix: What Terms Contribute to a Long-Range Potential? ........................... 199 Exercises ................................................................................................................200 References .............................................................................................................. 201
predictions of the energies and properties of unobserved levels and of a wide range of other types of data not considered in the original data analysis, including the collisional properties of the atoms forming the particular molecular state. This is possible for two reasons: (1) modern experimental methods often provide very high-quality data for vibrational levels spanning a large fraction of the potential well, and (2) the relevant Schrödinger equation is effectively one-dimensional, and can be solved efciently using standard numerical methods. This chapter takes the rst point for granted and focuses on how the experimental information thus obtained can be used to determine both precise and accurate equilibrium properties, and reliable overall potential energy functions for diatomic molecules.
