Knowledge Bank

The Born-Oppenheimer energy and the electric dipole and quadrupole moments are obtained as functions of nuclear geometry for the ground electronic state of $H+3$ by means of a Gaussian basis set with full configuration interaction. Vibrational basis functions are taken as eigenfunctions of one harmonic and two Morse model Hamiltonians whose potentials are fitted to cuts through the B-O energy surface corresponding to the three normal vibration coordinates. Improved vibrational basis functions are obtained by diagonalizing the Hamiltonian whose potential is the accurate B-O energy plus the rotational term containing the vibrational angular momentum of the degenerate modes. A vibrational-rotational configuration-interaction’’ calculation with products of these improved one-phonon’’ basis functions is then employed to obtain the effects of the remaining rotational perturbations, including mixing of the symmetric-top wave functions caused by asymmetric vibrations. The result is a set of wave functions in the electronic and nuclear coordinates, and energy levels, for the lowest 250 states of $H+3$. Ab initio values are obtained for the rotation-vibration spectroscopic constants, spectral frequencies, and the Einstein transition coefficients. The possibility of infrared detection of $H+3$ and some implications for molecular dynamics, properties of hydrogen plasmas, and composition of stellar atmospheres are discussed.