Gaussian functions in Hylleraas-configuration-interaction calculations. VI. The first excited state of H sup + sub 3

The Hylleraas-configuration-interaction (H-CI) method has been applied to the first {sup 3}{Sigma}{sup +}{sub {ital u}} excited state of the H{sup +}{sub 3} molecular ion. Besides the ground state, this is the only known bound state of H{sup +}{sub 3}, albeit with a very weak minimum of 8.428 kcal/mol. The equilibrium geometry and the minimum energy have been determined. The Hylleraas-CI energy of {minus}1.116 102 7 a.u. at an equidistant nuclear separation of 2.454 bohr is the lowest reported so far. The vibrational force constants and vibrational frequencies also have been computed.