Two-electron relativistic corrections to the potential energy surface and vibration–rotation levels of water

Two-electron relativistic corrections to the ground-state electronic energy of water are determined as a function of geometry at over 300 points. The corrections include the two-electron Darwin term (D2) of the Coulomb–Pauli Hamiltonian, obtained at the cc-pVQZ CCSD(T) level of theory, as well as the Gaunt and Breit corrections, calculated perturbationally using four-component fully variational Dirac–Hartree–Fock (DHF) wavefunctions and two different basis sets. Based on the calculated energy points, fitted relativistic correction surfaces are constructed. These surfaces are used with a high-accuracy ab initio nonrelativistic Born–Oppenheimer (BO) potential energy hypersurface to calculate vibrational band origins and rotational term values for H216O. The calculations suggest that these two-electron relativistic corrections, which go beyond the usual kinetic relativistic effects and which have so far been neglected in rovibrational calculations on light many-electron molecular systems, have a substantial influence on the rotation–vibration levels of water. The three effects considered have markedly different characteristics for the stretching and bending levels, which often leads to fortuitous cancellation of errors. The effect of the Breit interaction on the rovibrational levels is intermediate between the effect of the kinetic relativistic correction and that of the one-electron Lamb-shift effect.