Impact of nuclear quantum effects on the molecular structure of bihalides and the hydrogen fluoride dimer.

The structural impact of nuclear quantum effects is investigated for a set of bihalides, XHX, X = F, Cl, and Br, and the hydrogen fluoride dimer. Structures are calculated with the vibrational self-consistent-field (VSCF) method, the second-order vibrational perturbation theory method (VPT2), and the nuclear-electronic orbital (NEO) approach. In the VSCF and VPT2 methods, the vibrationally averaged geometries are calculated for the Born-Oppenheimer electronic potential energy surface. In the NEO approach, the hydrogen nuclei are treated quantum mechanically on the same level as the electrons, and mixed nuclear-electronic wave functions are calculated variationally with molecular orbital methods. Electron-electron and electron-proton dynamical correlation effects are included in the NEO approach using second-order perturbation theory (NEO-MP2). The nuclear quantum effects are found to alter the distances between the heavy atoms by 0.02-0.05 A for the systems studied. These effects are of similar magnitude as the electron correlation effects. For the bihalides, inclusion of the nuclear quantum effects with the NEO-MP2 or the VSCF method increases the X-X distance. The bihalide X-X distances are similar for both methods and are consistent with two-dimensional grid calculations and experimental values, thereby validating the use of the computationally efficient NEO-MP2 method for these types of systems. For the hydrogen fluoride dimer, inclusion of nuclear quantum effects decreases the F-F distance with the NEO-MP2 method and increases the F-F distance with the VSCF and VPT2 methods. The VPT2 F-F distances for the hydrogen fluoride dimer and the deuterated form are consistent with the experimentally determined values. The NEO-MP2 F-F distance is in excellent agreement with the distance obtained experimentally for a model that removes the large amplitude bending motions. The analysis of these calculations provides insight into the significance of electron-electron and electron-proton correlation, anharmonicity of the vibrational modes, and nonadiabatic effects for hydrogen-bonded systems.