We have developed the nuclear-electronic orbital (NEO) method for the incorporation of nuclear quantum effects and non-Born-Oppenheimer effects into quantum chemistry calculations.^{16, 17} In the NEO framework, specified nuclei are treated quantum mechanically on the same level as the electrons using molecular orbital techniques without invoking the Born-Oppenheimer separation between the electrons and the quantum nuclei. In this approach, the mixed nuclear-electronic time-independent or time-dependent Schrödinger equation is solved with wave function or density functional theory (DFT) methods. Typically the quantum nuclei are protons, although other nuclei and other types of particles such as positrons can also be treated quantum mechanically within this framework. An advantage of the NEO approach is that nuclear quantum effects such as delocalization, anharmonicity, and zero-point energy, as well as non-Born-Oppenheimer effects, are inherently included during geometry optimizations, reaction paths, and dynamics. We have written several reviews on the NEO method.^{273, 306}

Many of these NEO methods are in Q-Chem, and some are in GAMESS and Chronus Quantum.