13.5.1 Introduction

The nuclear-electronic orbital (NEO) method ¹³⁷⁰ Webb S. P., Iordanov T., Hammes-Schiffer S.
J. Chem. Phys.
(2002), 117, pp. 4106. Link ^{, 1003} Pavošević F., Culpitt T., Hammes-Schiffer S.
Chem. Rev.
(2020), 120, pp. 4222. Link provides the framework for the accurate and efficient description of multicomponent systems in which more than one type of particle is treated quantum mechanically. Typically, the NEO method treats all electrons and specified protons quantum mechanically on the same level with molecular orbital techniques. An advantage of the NEO method is that anharmonicity, proton delocalization, and zero point energy contributions of the quantum protons are included directly in the energy calculations, geometry optimizations, reaction paths, and dynamics. For a broad overview of the NEO framework and to help guide your selection, see the JCP perspective Ref.  495 Hammes-Schiffer S.
J. Chem. Phys.
(2021), 155, pp. 030901. Link and the Chemical Reviews article Ref.  1003 Pavošević F., Culpitt T., Hammes-Schiffer S.
Chem. Rev.
(2020), 120, pp. 4222. Link both by Hammes-Schiffer.