The nuclear-electronic orbital (NEO) method treats electrons and select nuclei quantum mechanically on the same level using an orbital-based formalism with the goal of obtaining a computationally tractable method that includes non-Born-Oppenheimer effects as well as nuclear quantum effects. The NEO method is ideal for studying chemical phenomena such as proton-coupled electron transfer (PCET) because the timescale for proton tunneling is often faster than the timescale for electronic transitions, thereby leading to a breakdown of the Born-Oppenheimer approximation. In applications of the NEO method to PCET, all electrons and one or a few protons are treated quantum mechanically, and a mixed nuclear-electronic time-independent Schrödinger equation is solved using explicitly correlated wavefunctions. Recent advances to the NEO method involving wavefunction and density functional theory will be discussed and benchmarking calculations on small molecules for basis sets will be presented.
