Exploring the bending vibrational bound state spectra of protium-, deuterium-, and tritium-oxide water isotopologues via symmetry-adapted Lie-algebraic Pöschl-Teller Hamiltonians
Abstract
Reliable bending mode spectroscopic constants - the harmonic wavenumber ωe and the anharmonicity constant xe - for triatomic building blocks are conspicuously absent from standard reference compilations such as those of Irikura (2007) and Shimanouchi (1972). This is the first of a series of articles anticipated to bridge this gap by extracting those hitherto unexplored constants for triatomics via Gaussian Process Regression (GPR) of literature-validated empirical band origins. This work, more specifically, focuses on this extraction for the three principal water isotopologues - H216O, D216O and T216O, - and exploration of bending vibrational bound state spectra via symmetry-adapted U(2) and U(3) Lie algebraic Pöschl-Teller (PT) Hamiltonians. The Dong-Lemus (2002) factorisation method is adopted to parameterise the analytically-solvable PT well, giving the potential strength λPT, range parameter a, dissociation depth De, zero-point energy EZPE, the maximum number of bound levels vmax, and the corresponding vibron number Nb. The U(2)⊃SO(2) and U(3)⊃SO(3)⊃SO(2) bending Hamiltonians are subsequently constructed, refined, and diagonalised to predict the entire bending overtone progression up to dissociation, together with the dipole transition intensities. The present analysis is restricted to the pure bending block (0,v2,0) of each isotopologue; inter-mode couplings (Fermi, Coriolis, Darling-Dennison) lie outside the 1-D bending Hamiltonian by construction and are treated as…
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