Accurate adiabatic correction in the hydrogen molecule

A new formalism for the accurate treatment of adiabatic effects in the hydrogen molecule is presented, in which the electronic wave function is expanded in the James-Coolidge basis functions. Systematic increase in the size of the basis set permits estimation of the accuracy. Numerical results for the adiabatic correction to the Born-Oppenheimer interaction energy reveal a relative precision of 10(-12) at an arbitrary internuclear distance. Such calculations have been performed for 88 internuclear distances in the range of 0 < R <= 12 bohrs to construct the adiabatic correction potential and to solve the nuclear Schrodinger equation. Finally, the adiabatic correction to the dissociation energies of all rovibrational levels in H-2, HD, HT, D-2, DT, and T-2 has been determined. For the ground state of H-2 the estimated precision is 3 x 10(-7) cm(-1), which is almost three orders of magnitude higher than that of the best previous result. The achieved accuracy removes the adiabatic contribution from the overall error budget of the present day theoretical predictions for the rovibrational levels. (C) 2014 AIP Publishing LLC.