Infrared spectrum quantum-mechanical calculation

The nitrosyldioxyl radical has largely been ignored in the chemical literature because it is relatively unstable in air. Nitrosyldioxyl radical is approximately 4.8 kcal/mol less stable than nitric oxide and oxygen in the gas phase less than 0.1% of the nitric oxide will combine with oxygen under standard conditions in the gas phase. Although present in low concentrations, the infrared spectrum of nitrosyldioxyl radical has been reported in the gas phase (Guillory and Johnston, 1965) and ab initio quantum mechanics calculations have been performed (Boehm and Lohr, 1989). 

The procedure of interpreting data concerning the molecule OPCl is described as an example. Fig. 4.4-3 shows the infrared spectrum of matrix-isolated OPCl with the two stretching vibrations at 1237.7 ( /(PO)) and at 489.4 cm (z/(PCl)). The deformation mode, of much lower intensity, lies at 308.0 cm. By using the precursor P OCl3, the absorptions are shifted to 1211.8, 484.7, and 298.0 cm respectively. These data confirmed the assignment of vibrations and the assumed sequence of the atoms O-P-Cl. Furthermore, by means of a normal coordinate analysis it was possible to limit the bond angle to a value of 105°, which is in accordance with the results of quantum-mechanical calculations. 

In addition to total energy and gradient, HyperChem can use quantum mechanical methods to calculate several other properties. The properties include the dipole moment, total electron density, total spin density, electrostatic potential, heats of formation, orbital energy levels, vibrational normal modes and frequencies, infrared spectrum intensities, and ultraviolet-visible spectrum frequencies and intensities. The HyperChem log file includes energy, gradient, and dipole values, while HIN files store atomic charge values. 

The theory of electron-transfer reactions presented in Chapter 6 was mainly based on classical statistical mechanics. While this treatment is reasonable for the reorganization of the outer sphere, the inner-sphere modes must strictly be treated by quantum mechanics. It is well known from infrared spectroscopy that molecular vibrational modes possess a discrete energy spectrum, and that at room temperature the spacing of these levels is usually larger than the thermal energy kT. Therefore we will reconsider electron-transfer reactions from a quantum-mechanical viewpoint that was first advanced by Levich and Dogonadze [1]. In this course we will rederive several of, the results of Chapter 6, show under which conditions they are valid, and obtain generalizations that account for the quantum nature of the inner-sphere modes. By necessity this chapter contains more mathematics than the others, but the calculations axe not particularly difficult. Readers who are not interested in the mathematical details can turn to the summary presented in Section 6. 

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