DETERMINATION OF THE VIBRATIONAL CONSTANTS OF SOME DIATOMIC-MOLECULES - COMBINED INFRARED SPECTROSCOPIC AND QUANTUM CHEMICAL 3RD YEAR CHEMISTRY PROJECT

The table indicates that the values of the molecular constants v0, αe, Be, re, and k obtained in the experimental part are in fairly good agreement with those given in the literature by Herzberg (2) and by Banwell (3). The measured band intensities of HCl and HBr do not differ greatly from those in the literature (4), but those of CO and NO are in much wider disagreement with the particular literature values quoted (4, 5). However, there is a fairly wide disparity among the numerous intensities reported in the literature for these two molecules, and in any case the measurement of intensities in the infrared is notoriously difficult to accomplish accurately (14). The calculated positions of the Morse curve energy minima, re, are also in reasonable agreement with literature values. However the absolute values of the dissociation energies, De, are consistently a factor of ∼5 too high for the singly bonded molecules HC1 and HBr and ∼25 times too high for the multiply bonded molecules CO and NO, although the order of dissociation energies of CO > NO > HCl > HBr is reproduced faithfully. Similarly the calculated absolute values of the force constants, k, are very close to a factor of 2 too high for the closed shell molecules HCl, HBr, and CO and a little over three times too high for the open shell molecule NO, although here the correct sequence of force constant values is not reproduced because of the overestimated figure for NO. The force constant and dissociation energy, however, depend on the determination of the total molecular energy and it is well-known that the CNDO/2 method is least sensitive for determining those quantities which depend on the absolute values of the energy (15). Likewise the dipole moments calculated at the equilibrium geometry differ by a considerable percentage for HCl, HBr, and CO, although for NO, agreement is reasonably close. In view of the lack of agreement between the calculated and literature dipole moments, it is not surprising that the CNDO/2 calculated dipole moment derivatives are at variance with those calculated from the absolute intensity values found in the literature (4,5), except, possibly, for HBr. This feature must also be attributed to shortcomings in the CNDO/2 procedure. Notwithstanding the lack of agreement between the numerical values of the molecular constants determined experimentally, by a standard physical chemistry experiment (1), and theoretically, using the well-known semi-empirical CNDO/2 method (16), the utility of this project lies in the blending together of an easily understandable and readily performed manipulative procedure with a rather more esoteric, although still easily carried out computational exercise, all this involving material which is entirely relevant to the lecture course. Each part complements the other, one illustrating the theoretical background on which the other draws, and the other providing the experimental evidence for the quantum chemical predictions of the first. The project can be easily extended to include different molecules for different students, or in different years, the only limitation being the availability of suitable gaseous diatomic molecules which are easily handled and yield useful infrared spectra. It is rare in physical chemistry to find such a neat example of the coupling of the experimental with the theoretical branches of the discipline. The CNDO/2 programs (11, 12) are obtainable from the Quantum Chemistry Program Exchange. Listings of the band area measurement program, and of the program for determining the Morse curve parameters using the Newton-Raphson method, may be obtained from the author.