Abstract
Highly accurate wave functions of the ground and electronic (1s ? g and 3d ? g ), vibrational (v = 0-15 for 1s ? g and v = 0-8 for 3d ? g ), and rotational (L = 0-6: 1 S, 3 P, 1 D, 3 F, 1 G, 3 H, and 1 I) excited states of the hydrogen molecular ion were obtained by solving the non-Born-Oppenheimer (non-BO) Schr?dinger equation using the free complement (FC) method. The vibronic states belonging to the electronic excited state 3d ? g are embedded in the continuum of the dissociation, H(1s) + H+. Nevertheless, they exist as physical bound states that have negligible coupling with the continuum. The complex scaled Hamiltonian was employed to analyze the bound and/or resonance natures of the obtained eigenstates, and a new resonance state appeared between the above two electronic states. We numerically proved that the FC method is a reliable theoretical tool for investigating non-BO quantum effects, and it should be available for various studies of hydrogen-related space chemistry and low-temperature physics.
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