H3 +: <i>A</i> <i>b</i> <i>i</i> <i>n</i> <i>i</i> <i>t</i> <i>i</i> <i>o</i> calculation of the vibration spectrum

Abstract

The vibration spectrum of H3 + is calculated from the representation of a previously reported [J. Chem Phys. 60, 4251 (1974)] ab initio potential-energy surface in a fifth degree Simons–Parr–Finlan (SPF) expansion. Morse- and harmonic-oscillator basis functions are used to describe the motions of the three oscillators and the Harris–Engerholm–Gwinn quadrature technique is used to obtain matrix elements of the Hamiltonian in the basis of vibrational configurations. Our variational method is thus analogous to configuration– interaction calculations for electronic states. The ground state is found to have a zero-point energy of 4345 cm−1 and a vibrationally averaged geometry of R1=R2=0.91396 Å, ϑ=60.0012°, where ϑ is the angle between the two equivalent bonds. The transition frequencies for the E and A1 fundamentals are ?E=2516 cm−1 and ?A=3185 cm−1 and those for the corresponding first overtones of the bending mode are 2?E=5004±4 cm−1 and 2?A=4799 cm−1. The first overtone of the breathing mode is 6264 cm−1. The first-excited A1 vibration state is metastable with a dipole–radiation lifetime of 3 sec. Transition frequencies, Einstein coefficients, and lifetimes are reported for a total of 21 transitions. Analysis of results for Dunham number and normal-coordinate expansions in comparison with those for SPF expansion show the latter to be superior for ab initio vibrational calculations. A scheme for possible direct measurement of the fundamental A1 and E vibrational bands is suggested.