ASSIGNMENT OF VIBRATION-ROTATION SPECTRA OF $H^{+}_{3}$ AND $D^{+}_{3}$ USING MORSE-BASED DISCRETE-VARIABLE-REPRESENTATION CALCULATIONS
Loading...
Date
1993
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University
Abstract
For the higher rotational and vibrational levels of $H^{+}_{3}$ and $D^{+}_{3}$ the effective Hamiltonian approach used in earlier work ceases to be very effective. The present calculations use a Morse-based discrete variable representation for the three internuclear distances $r_{1}, r_{2}, r_{3}$ as internal coordinates, and the ab initio potential surface of Meyer, Botschwina and $Burton^{1}$ with adjustments of 6 of the 24 potential constants to fit the observed data. The calculations are done in two steps. A large-basis vibrational calculation is performed first, the unphysical configurations of the types $r_{1} < 0$ or $r_{1} > r_{j} + r_{k}$ being avoided by giving them arbitrarily high potential energies. Then the vibration-rotation levels are calculated using a basis of symmetrised products of rotational wavefunctions with the lower vibrational eigenfunctions. The adjustment of the potential makes it possible to assign about 30 and 400 new infrared lines of $H^{+}_{3}$ (total 448) and $D^{+}_{3}$ (total 496), respectively, observed by the groups in $Ottawa^{2}$ and $Chicago^{3}$. The present data set contains levels with up to two vibrational quanta only, including the first observation of the $2\nu_{2}$ band of $D^{+}_{3}$. $^{4}Levels$ with $\nu_{1} + \nu_{2} = 3$ will require more potential constants to be adjusted. The present boundary conditions at the linear configuration are not exact, and a different coordinate system (such as hyperspherical coordinates) will probably be required for levels with $\nu_{1} + \nu_{2} > 3$ for $H^{+}_{3}$ or 5 for $D^{+}_{3}$.
Description
$^{1}$ W. Meyer, P. Botschwina and P. Burton, J. Chem. Phys. 84. 891-900 (1986). $^{2}$ A. R. W. McKellar, T. Amano, W. A. Majewski, S. Civis, and M.-C. Chan. 3. T. Oka, C. Gabrys, L.-W. Xu, B. Ventrudo, S. S. Lee, D. Uy, and M.-F. Jagod. 4 M.-C. Chan, J. K. G. Watson, and T. Amano, this conference.
Author Institution: Herzberg Institute of Astrophysics., National Research Council of Canada
Author Institution: Herzberg Institute of Astrophysics., National Research Council of Canada