Electron-nuclear coupling in the hyperfine structure of the hydrogen molecular ion

A perturbation theory for determining the electron-nuclear coupling corrections to the adiabatic expectation values of operators of molecular systems is developed and applied to the hyperfine Hamiltonian of the hydrogen molecular ion. The expectation values of the Fermi contact parameter for the rotation-vibration states N=1, v=4--8 are compared with experimental results. Previous adiabatic expectation values differ from the empirical values by about 600 kHz. Inclusion of the first-order corrections reduces the discrepancies to less than 9 kHz