Multicomponent quantum chemistry methods allow the analysis of nuclear as well as electronic orbitals in molecular systems. The nuclear-electronic orbital (NEO) approach treats specified nuclei, typically protons, quantum mechanically on the same level as the electrons with multicomponent density functional theory (DFT) or wave function methods. Within the NEO-DFT framework, electron-proton correlation is essential for describing accurate proton densities and energies. Analysis of the electronic and protonic orbitals along the minimum energy path for hydrogen transfer and proton-coupled electron transfer (PCET) reactions indicates whether the electrons and protons move synchronously or asynchronously. Multicomponent time-dependent DFT (NEO-TDDFT) provides accurate electronic, proton vibrational, and electron-proton vibronic excitations, which can be characterized by the corresponding transition densities. Multicomponent wave function methods based on coupled cluster and orbital-optimized perturbation theory approaches also produce accurate proton densities and energies, and multicomponent equation-of-motion coupled cluster methods produce accurate electronic, vibrational, and vibronic states excitation energies. Multistate NEO-DFT methods enable the calculation of bilobal, delocalized proton densities and tunneling splittings for hydrogen tunneling systems. Real-time NEO-TDDFT methods combined with Ehrenfest dynamics allow nonequilibrium nuclear-electronic dynamics beyond the Born-Oppenheimer approximation. The electronic and protonic densities can be visualized during the nonadiabatic dynamics trajectories to illustrate the fundamental mechanisms of hydrogen transfer and PCET. Thus, the analysis of protonic as well as electronic orbitals within the NEO framework provides insights into a wide range of chemical phenomena.

Electronic and protonic orbitals in multicomponent quantum chemistry

ACS Fall 2021

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