Solving the non-Born-Oppenheimer Schrödinger equation for the hydrogen molecular ion with the free complement method. II. Highly accurate electronic, vibrational, and rotational excited states

Abstract

Highly accurate wave functions of the ground and electronic (1s σ g and 3d σ g ), vibrational (v = 0-15 for 1s σ g and v = 0-8 for 3d σ 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) Schrödinger equation using the free complement (FC) method. The vibronic states belonging to the electronic excited state 3d σ 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. © 2013. The American Astronomical Society. All rights reserved..