Three‐body molecular states of the LiH2+ system in the Born–Oppenheimer approximation

• Published in: International journal of quantum chemistry 2018-08, Vol.118 (15), p.n/a
• Main Authors: Randazzo, Juan M., Aguilar‐Navarro, Antonio
• Format: Article
• Language: English
• Subjects: Approximation; Born–Oppenheimer; bound states; Chemistry; Electron states; Mathematical analysis; Molecular chains; Physical chemistry; Potential energy; potential energy surface; Quantum mechanics; reactive scattering; Sturmian functions; Wave functions
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.25611

In this work, we present a quantum mechanical treatment of the three‐body LiH2+ molecular system in the Born–Oppenheimer (BO) approximation, were the nuclei dynamics is evaluated over the potential energy surfaces (PES) induced by the electronic states. The PES corresponding to the two lowest electronic levels are the ones described by Martinazzo et al. (Chem. Phys. 2003, 287, 335), and are used to write the three‐body Schrdinger equation of the three atomic system. We use the generalized Sturmian functions method to expand the wave functions in each (distinguishable) pair of relative coordinates or Jacobi pairs, and analyze the convergence differences between the series. A partial‐wave decomposition of the potential is proposed to simplify the Hamiltonian matrix element calculation. Bound states are considered for the ground and first excited electronic PES, the spreading of energies after sudden electronic transitions studied, and the break‐up probability induced by the sudden change of the PES evidenced. In molecular calculations, atomic cores are generally viewed as point particles, fixed in space or oscillating around an equilibrium position. A quantum mechanical treatment of the three‐body LiH2+ molecule, where the the interaction potential comes from a potential energy surface, provides the complete description of the system within the Born–Oppenheimer approximation.