Multicomponent Quantum Chemistry: Integrating Electronic and Nuclear Quantum Effects via the Nuclear–Electronic Orbital Method

Abstract

In multicomponent quantum chemistry, more than one type of particle is treated quantum mechanically with either density functional theory or wave function based methods. In particular, the nuclear-electronic orbital (NEO) approach treats specified nuclei, typically hydrogen nuclei, on the same level as the electrons. This approach enables the incorporation of nuclear quantum effects, such as nuclear delocalization, anharmonicity, zero-point energy, and tunneling, as well as non-Born–Oppenheimer effects directly into quantum chemistry calculations. Such effects impact optimized geometries, molecular vibrational frequencies, reaction paths, isotope effects, and dynamical simulations. Multicomponent density functional theory (NEO-DFT) and time-dependent DFT (NEO-TDDFT) achieve an optimal balance between computational efficiency and accuracy for computing ground and excited state properties, respectively. Multicomponent wave function based methods, such as the coupled cluster singles and doubles (NEO-CCSD) method for ground states and the equation-of-motion counterpart (NEO-EOM-CCSD) for excited states, attain similar accuracy without requiring any parametrization and can be systematically improved but are more computationally expensive. Variants of the orbital-optimized perturbation theory (NEO-OOMP2) method achieve nearly the accuracy of NEO-CCSD for ground states with significantly lower computational cost. Additional approaches for computing excited electronic, vibrational, and vibronic states include the delta self-consistent field (NEO-ΔSCF), complete active space SCF (NEO-CASSCF), and nonorthogonal configuration interaction methods. Multireference methods are particularly important for describing hydrogen tunneling processes. Other types of multicomponent systems, such as those containing electrons and positrons, have also been studied within the NEO framework. The NEO approach allows the incorporation of nuclear quantum effects and non-Born–Oppenheimer effects for specified nuclei into quantum chemistry calculations in an accessible and computationally efficient manner.

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

“… 64 In certain cases, semiclassical treatments are appropriate; for example, nonadiabatic effects between electrons and nuclei can be considered using nuclear-electronic orbital methods. 65 …”

Molecular second-quantized Hamiltonian: Electron correlation and non-adiabatic coupling treated on an equal footing

“…Explicitly correlated methods can help to reduce basis set dependence at the cost of increased complexity. Overall, this approach is best for small nuclei like H. 27 Similar ideas can be found in the world of theoretical attosecond spectroscopy, where the energy bandwidth of a pulse covers multiple electronic states and can lead to photoionisation. 44 Strong coupling to an external pulse causes significant changes in electronic and nuclear dynamics, necessitating multiconfigurational representation of the wavefunction.…”

“…They treat each nucleus as a quantum particle alongside the electrons, and solve generalised Hartree-Fock (HF) equations in a basis of single particle functions. [23][24][25][26][27] For electrons, these are the standard atomic orbitals (AO) resulting in molecular orbitals (MO); for the nuclei, an analogous basis of Gaussian type functions is used, resulting in nuclear orbitals. The molecular Hilbert space is spanned by symmetrised products of nuclear and molecular orbitals, so that particles follow correct fermionic or bosonic statistics depending on their spin.…”

Time-dependent variational dynamics for nonadiabatically coupled nuclear and electronic quantum wavepackets in molecules

“…Finally, we slightly touch upon the works of nuclear-electronic orbital methods, mainly developed in quantum chemistry as a direct extension of the molecular orbital model. We simply refer to the review article by Pavošević, Culpitt, and Hammes-Schiffer [51], and extensive citation in it, including Thomas. [52] and Nakai et al [53].…”