13.5.1 Introduction

The nuclear-electronic orbital (NEO) method provides the framework for the accurate and efficient description of multicomponent systems in which more than one type of particle is treated quantum mechanically. ¹³⁷³ Webb S. P., Iordanov T., Hammes-Schiffer S.
J. Chem. Phys.
(2002), 117, pp. 4106. Link ^{, 1006} Pavošević F., Culpitt T., Hammes-Schiffer S.
Chem. Rev.
(2020), 120, pp. 4222. Link 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. Comprehensive reviews of the NEO framework can be found elsewhere. ¹⁰⁰⁶ Pavošević F., Culpitt T., Hammes-Schiffer S.
Chem. Rev.
(2020), 120, pp. 4222. Link ^{, 495} Hammes-Schiffer S.
J. Chem. Phys.
(2021), 155, pp. 030901. Link