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T. A. Ford universitv of the Wltwatersrand ~ohannesbuq.2001. South Africa
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Determination of the Vibrational Constants of Some Diatomic Molecules A combined infrared spectroscopic and quantum chemical third year chemistry project
Students in the third year advanced course of the four year honors chemistry program a t this university take a 13lecture component on molecular spectroscopy. This part of the course deals with nuclear magnetic resonance spectroscopy, and the rotational, vibrational, electronic, and photoelectron spectroscopies of diatomic molecules. I n addition, students undertake one laboratory project during the year designed to occupy them for ten 3-hr laboratory periods, which counts for 6% of their total year's mark. In one of the optionsfor this project, the rotation-vibration infrared spectra of a number of gaseous diatomic molecules were recorded, from which the fundamental vibrational wavenumber, io, the force constant, k, the rotation-vibration interaction constant, a,, the equilihrium rotational constant, Be, and the equilihrium internuclear distance, re, were determined. T h e intensities of the fundamental absorption bands were then measured using nitrogen, in each case, as a pressure-broadening gas. From the measured intensities, the changes of dipole moment with change of bond length a t the equilibrium value, (aplar),=,, were calculated. Several of these vihrational constants could also he calculated using the CNDOh semi-empirical molecular orbital procedure. By calculating the total energy and the dipole moment of each molecule as a function of its bond length, plots could he ohtained of each property. By fitting the energy versus hond length graphs to the Morse curve by a non-linear least-squares technique, the three parameters r.P. (the bond dissociation energy), and a, where a = (k/2DJ112, could be determined, and in the case of the equilibrium internuclear distance and the force constant, compared with those determined experimentally. In the caseof the dipole moment versus bond length curves, a least-squares fit was ohtained with a cubic function and the analytical derivative a t r = re yielded the quantity (dplar),=,, which again could he compared with that obtained in the experimental section. Finally the dissociation energy derived from the Morse curve and dipole moment calculated a t the equilibrium (literature) hond length could be compared with those found in the literature. Experimental Section The spectra of hydrogen chloride, hydrogen bromide, carbon monoxide, and nitric oxide, ohtained commercially in lecture bottle auantities. were recorded usine a Perkin Elmer model 521 .eratine . ~,. infrared spectrophc~cometer,using standard gas rell.i. The mtmimal fine itrurturr of HCI, Hnr, and CO rlenrly showed the expected I'tl pattern whilr in the case of NO. 1'. Q,and I( brdnvhei urw clearly r~sihle.T ~ mprhd P ot trearmg the spectra in order t u yield the \ i hrational mnstants referred to nhwe is desvrihpd fully by Sh
