The Born-Oppenheimer energies of teh fourth 1Σg+ state of hydrogen are computed over the range 1 < R ≤ 20 a.u. The lowest vibration-rotation levels are localized near the minimum of the potential curve (R {reversed tilde equals} 2 a.u.) and can be correlated with the experimental levels of the state (1sσ3sσ) H1Σg+ of H2. In the region around R = 11 a.u. the potential curve exhibits a local minimum which gives rise to predicted stable rotation-vibration levels designated H1Σg+. These levels should be observable via infrared combinations with very high vibrational levels of the B1Σu+ state. The electronic H - B transition moment zH,B is computed and is found to have a maximum of large magnitude (zH,B {reversed tilde equals} 4 a.u.) near R = 11 a.u. The vibrational transition moments H,v′ - B,v″ are computed for the most relevant v′-v″ combinations. The predissociation of the H levels by nuclear dynamic coupling with the EF continuum is estimated to be ineffectual. Similar conclusions regarding transition moments and predissociation are predicted to hold for optical B1Σu+ - EF1Σg+ transitions and B-B predissociation. © 1979.