The calculation of molecular energy level sums and densities is necessary for the treatment of many physical and chemical problems including reaction rates. An extension of Beyer and Swinehart's algorithm for directly computing harmonic oscillator eigenstate sums and densities is described. With this new algorithm it is possible to compute exact or near-exact energy level sums and densities for degrees of freedom such as free and hindered rotors and anharmonic oscillators so long as the energy levels for each degree of freedom can be specified. Computer calculation by this technique is practical even for large molecules up to all chemically interesting energies and error is confined to small rounding errors. Results by this algorithm are compared to values of energy level sums that have been given in the literature by various alternative approximate treatments and permit more rigorous testing of the latter and assessment of the approximations involved.
Some exact sums of harmonic vibrational-energy-level densities for 45 molecules were obtained at various energies with a digital computer. An improved ``corresponding vibrational states'' type of approximation to these sums at low and moderate energies is described. The approximation has the great advantage or being very rapid, of requiring scarcely any calculational detail and of using the actual molecular frequencies. The agreement of the approximation with a smoothed true count is usually within a few percent at quite low energies, ε≳0.1 εz. It has the further advantage of being good also for the difficult case of a complex polyatomic molecule with noncommensurable frequencies.
The behavior of the sums for various vibrational patterns is considered. The importance of noncommensurability and number of frequency groups is displayed.
We have described the concept of using the aqueous humor glucose as a measure of the blood glucose concentration, with a view to developing a noninvasive glucose monitor for diabetic individuals. We have conceived of a scleral lens that houses a light source, polarizers, other electro-optic units, and a light detector, and which measures the optical rotation of the aqueous humor continuously. We have built an optical bench mock-up of the glucose sensor and assessed the limits of its capabilities. We have described a physical method, employing the Faraday effect, that modulates the incident light and uses a compensator to introduce a feedback mechanism giving a null-point technique capable of measuring extremely small rotations with an accuracy of 0.4 s of arc. We have used this and have measured the optical rotations of glucose solutions from 0.02 to 0.1%, and have demonstrated linearity in both cases. Miniaturization of the technique is discussed.
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