Nuclear-electronic orbital (NEO) method

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.

Multicomponent wave function methods

NEO-HF (multiple protons, vibrational analysis) 54, 57, 125


NEO-MP2 70, 270

NEO-OOMP2, NEO-SOS-OOMP2 (orbital optimized MP2) 270

NEO-CCSD (coupled-cluster singles and doubles, Brueckner doubles, orbital-optimized CCD, lambda equations, density fitting) 246, 259, 270, 298

NEO-UCC (unitary coupled cluster) 302

NEO-EOM-CCSD (frequency and time domain equation-of-motion) 252, 282

NEO-NOCI (nonorthogonal CI) 75


Multicomponent DFT methods

NEO-DFT 96, 105, 118

Electron-proton correlation functionals (epc17, epc18, epc19) 231, 232, 238, 264

NEO-TDDFT 236, 255

NEO-TDDFT analytical gradients 308

NEO-MSDFT (multistate DFT) 288

Real-time NEO-TDDFT (Ehrenfest dynamics) 275, 291, 300

Additional NEO features

Analytical Hessians, transition states, minimum energy paths (NEO-HF, NEO-DFT) 297, 308

Stability conditions and local SCF solutions 239

Molecular vibrational frequencies (NEO-DFT(V)) 250, 266

Diagonal Born-Oppenheimer corrections 258

Early NEO methods (less relevant)

NEO explicitly correlated methods with Gaussian-type geminal functions (XCHF and RXCHF) 86, 103, 108, 142, 167, 192, 193 

NEO explicitly correlated methods applied to positrons 100, 112, 154, 168, 220

Electron-proton correlation functionals (explicitly correlated-based) 105, 145, 155

NEO-FMO (fragment molecular orbital) 123

NEO vibronic coupling theory for H tunneling splittings 111

NEO isotope effects 73