Numerical integration, vibrational averaging

For diatomic molecules, if the potential curve is known, numerical vibrational wavefunctions can be determined by the standard Numerov-Cooley technique [49] and for which computer programmes are available [50], The vibrational averaging for any state is then simply the numerical integration of , where v> is the vibrational wavefunction for the state of interest (usually the ground state). This, obviously, requires knowledge of the property P for a number of intemuclear separations (R). Alternatively, simple perturbation... 

Typically 60-150 ns after the photodissociation pump pulse, nascent OH product radicals were probed by a second copropagating UV probe laser beam by LIF in the A Z" - X H system as schematically depicted in Fig. 1. The probe beam with a bandwidth of 0.2 cm was provided by a frequency-doubled dye laser, pumped by a XeCl excimer laser and was tunable in the wavelength region 305-320 nm in order to scan OH LIF excitation spectra. Line positions for the different OH fine-structure transitions were taken from Ref. 30. Both lasers were operated at 20 Hz and each data point in a LIF excitation spectrum was obtained by averaging the collected fluorescence signal over 40-80 laser shots. The measured LIF spectra were stored on a computer for further data processing. OH vibrational and rotational fine-structure state distributions were determined by numerical integration of... 

Numerical evaluation of the Kassel integral permitted a comparison between theoretical and experimental fall-off behaviour . With an average molecular diameter of 5.5 A the calculated rate coefficient-azoethane pressure curve showed the best agreement with experiment at an effective number of oscillators of 18, somewhat less than half of the maximum 2N— 6. Because of the complexity of the reaction the experimental curve is probably in error, rendering comparison unreliable. Similar calculations for azomethane using the earlier uninhibited kinetic data showed best agreement with experiments at a molecular diameter of 4.7 A and an effective number of oscillators of 12, one half of the total normal modes of vibrations. 

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