Solving non-Born–Oppenheimer Schrödinger equation for hydrogen molecular ion and its isotopomers using the free complement method

Yuh Hijikata, Hiroyuki Nakashima, Hiroshi Nakatsuji
2009 Journal of Chemical Physics  
The Schrödinger equations for the hydrogen molecular ion ͑H 2 + ͒ and its isotopomers ͑D 2 + , T 2 + , HD + , HT + , and DT + ͒ were solved very accurately using the free iterative complement interaction method, which is referred to in short as the free complement ͑FC͒ method, in the non-Born-Oppenheimer ͑non-BO͒ level, i.e., in the nonrelativistic limit. Appropriate complement functions for both electron and nuclei were generated automatically by the FC procedure with the use of the non-BO
more » ... e of the non-BO Hamiltonian, which contains both electron and nuclear operators on an equal footing. Quite accurate results were obtained not only for the ground state but also for the vibronic excited states. For example, we obtained the ground-state energy of H 2 + as −0.597 139 063 123 405 074 834 134 096 025 974 142 a.u., which is variationally the best in literature. The difference in the nuclear spin states of 1 S ͑para͒ and 3 P ͑ortho͒ of H 2 + and some physical expectation values for several of the isotopomers shown above were also examined. The present study is the first application of the FC method to molecular systems with the non-BO Hamiltonian.
doi:10.1063/1.3048986 pmid:19154014 fatcat:msspdhdvenfpzbjsouqidzryzm