Rigid rotor-harmonic oscillator approach

Except for floppy molecules, thermal contributions at room temperature can be quite accurately evaluated using the familiar rigid rotor-harmonic oscillator (RRHO) approach. If data at high temperatures are required, this approach is no longer sufficient, and an anharmonic force field and analysis, combined with a procedure for obtaining the rotation-vibration partition function therefrom, are required. Two practical procedures have been proposed. The first one, due to Martin and co-workers " is based on asymptotic expansions for the nonrigid rotor partition function inside an explicit loop over vibration. It yields excellent results in the medium temperature range but suffers from vibrational level series collapse above 2000 K or more. A representative application (to FNO and CINO) is found in Ref. 42. 

In order to illustrate the role played by entropy S in adsorption processes, the entropy change AaS accompanying the adsorption in a very simple case was computed, by using the standard statistical mechanics rigid rotor/harmonic oscillator formula[94]. In Fig. 1.18 the adsorption of an Ar atom at the surface of an apolar solid is schematically illustrated. The Ar atom approaches the solid surface from the gas phase the translation entropy of the solid, which is fixed in the space, is taken as zero, whereas the free Ar atoms, before interacting with the solid surface, possess a translational entropy St which amounts to 150 and 170 J moP at T = 100 and 298K, respectively, at pAr = 100 Torr. 

Recently, the above approach has been applied to systems with a collection of harmonic oscillators coupled with rigid rotors and systems with a collection of anharmonic oscillators by Tou and Lin. For a system with a collection of w harmonic oscillators. . . , g, . . . g ) coupled... 

With the above approach we can combine the use of curvilinear normal coordinates with the Eckart frame. When we do so, the harmonic oscillator, rigid rotor, and, to lowest order, the Coriolis and centrifugal coupling contributions to H have exactly the same form as those found for the more commonly used Watson Hamiltonian (58). 

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