Diagonal Born--Oppenheimer correction in strong magnetic fields: finite-difference approach for light diatomic molecules

Abstract

The influence of the diagonal Born--Oppenheimer correction (DBOC) on the electronic structure of light diatomic molecules subjected to strong magnetic fields is investigated. H$_2$, HeH$^+$, and LiH are considered, using both the Hartree--Fock (HF) approximation and configuration interaction with single and double excitations (CISD). The analysis covers magnetic field strengths up to $B_\parallel = 0.2$ a.u. ($4.7\times10^{4}$~T), relevant to astrophysical conditions near magnetic white dwarfs. Although the correction noticeably shifts total electronic energies, it varies smoothly with internuclear distance and depends only weakly on the field, so that it enters the vibrational transition frequencies as a nearly field-independent offset, shifting the fundamental interval by about $1$~cm$^{-1}$ and the higher levels by up to $15$ cm$^{-1}$. These shifts exceed the $0.1$--$2.0$ cm$^{-1}$ accuracy currently attainable for molecular lines in the atmospheres of magnetic white dwarfs. Comparison of HF and CISD results shows that electron correlation has a non-negligible effect on the DBOC, most pronounced for the strongly ionic LiH bond.