Nonadiabatic Dynamics of Hydrogen Tunneling with Nuclear-Electronic Orbital Multistate Density Functional Theory

Squeezed Protons and Infrared Plasmonic Resonance Energy Transfer

Unusual nuclear quantum effects may emerge near noble metal nanostructures such as squeezed vibrational states in molecular junctions and plasmonic resonance energy transfer in the infrared domain. Herein, nuclear quantum effects near heavy metals are studied by nuclear-electronic orbital density functional theory (NEO-DFT) with an effective core potential. For a quantum proton sandwiched between a pair of gold tips modeled by two Au6 clusters, NEO-DFT calculations suggest that the quantum proton density can be squeezed as the tip distance decreases. For an HF molecule placed near a one-dimensional Au nanowire composed of up to 34 Au atoms, real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) shows that the infrared plasmonic motion within the Au nanowire may resonantly transfer electronic energy to the HF proton vibrational stretch mode. Overall, these calculations illustrate the advantages of the NEO approach for probing nuclear quantum effects, such as squeezed proton vibrational states and infrared plasmonic resonance energy transfer.

Nuclear-Electronic Orbital Quantum Mechanical/Molecular Mechanical Real-Time Dynamics

Simulating the nuclear-electronic quantum dynamics of large-scale molecular systems in the condensed phase is key for studying biologically and chemically important processes such as proton transfer and proton-coupled electron transfer reactions. Herein, the real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) approach is combined with a hybrid quantum mechanical/molecular mechanical (QM/MM) strategy to enable the accurate description of coupled nuclear-electronic quantum dynamics in the presence of heterogeneous environments such as solvent or proteins. The densities of the electrons and quantum protons are propagated in real time, while the other nuclei are propagated classically on the instantaneous electron-proton vibronic surface. This approach is applied to phenol bound to lysozyme, intramolecular proton transfer in malonaldehyde, and nonequilibrium excited-state intramolecular proton transfer in o-hydroxybenzaldehyde. These examples illustrate that the RT-NEO-TDDFT framework, coupled with an atomistic representation of the environment, allows the simulation of condensed-phase systems that exhibit significant nuclear quantum effects.

Proton transfer kinetics of transition metal hydride complexes and implications for fuel-forming reactions

Proton transfer reactions involving transition metal hydride complexes are prevalent in a number of catalytic fuel-forming reactions, where the proton transfer kinetics to or from the metal center can have significant impacts on the efficiency, selectivity, and stability associated with the catalytic cycle. This review correlates the often slow proton transfer rate constants of transition metal hydride complexes to their electronic and structural descriptors and provides perspective on how to exploit these parameters to control proton transfer kinetics to and from the metal center. A toolbox of techniques for experimental determination of proton transfer rate constants is discussed, and case studies where proton transfer rate constant determination informs fuel-forming reactions are highlighted. Opportunities for extending proton transfer kinetic measurements to additional systems are presented, and the importance of synergizing the thermodynamics and kinetics of proton transfer involving transition metal hydride complexes is emphasized.

Nonadiabatic Nuclear-Electron Dynamics: A Quantum Computing Approach

Coupled quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent representations of electrons and nuclei also exist, which do not rely on any a priori approximation. However, their implementation is hampered by prohibitive scaling. Consequently, quantum computers offer a unique opportunity for extending their use to larger systems. Here, we propose a quantum algorithm for simulating the time-evolution of molecular systems and apply it to proton transfer dynamics in malonaldehyde, described as a rigid scaffold. The proposed quantum algorithm can be easily generalized to include the explicit dynamics of the classically described molecular scaffold. We show how entanglement between electronic and nuclear degrees of freedom can persist over long times if electrons do not follow the nuclear displacement adiabatically. The proposed quantum algorithm may become a valid candidate for the study of such phenomena when sufficiently powerful quantum computers become available.

Generalized Nuclear-Electronic Orbital Multistate Density Functional Theory for Multiple Proton Transfer Processes

Proton transfer and hydrogen tunneling play pivotal roles in many chemical and biological processes. The nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) approach was developed to describe hydrogen tunneling systems within the multicomponent NEO framework, where the transferring proton is quantized and treated with molecular orbital techniques on the same level as the electrons. Herein, the NEO-MSDFT framework is generalized to an arbitrary number of quantum protons to allow applications to systems involving the transfer and tunneling of multiple protons. The generalized NEO-MSDFT approach is shown to produce delocalized, bilobal proton densities and accurate tunneling splittings for fixed geometries of the formic acid dimer and asymmetric substituted variants, as well as the porphycene molecule. Investigation of a protonated water chain highlights the applicability of this approach to proton relay systems. This work provides the foundation for nuclear-electronic quantum dynamics simulations of a wide range of multiple proton transfer processes.

Surface hopping modeling of charge and energy transfer in active environments

An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.

Electronic Born-Oppenheimer approximation in nuclear-electronic orbital dynamics

Within the nuclear-electronic orbital (NEO) framework, the real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) approach enables the simulation of coupled electronic-nuclear dynamics. In this approach, the electrons and quantum nuclei are propagated in time on the same footing. A relatively small time step is required to propagate the much faster electronic dynamics, thereby prohibiting the simulation of long-time nuclear quantum dynamics. Herein, the electronic Born-Oppenheimer (BO) approximation within the NEO framework is presented. In this approach, the electronic density is quenched to the ground state at each time step, and the real-time nuclear quantum dynamics is propagated on an instantaneous electronic ground state defined by both the classical nuclear geometry and the nonequilibrium quantum nuclear density. Because the electronic dynamics is no longer propagated, this approximation enables the use of an order-of-magnitude larger time step, thus greatly reducing the computational cost. Moreover, invoking the electronic BO approximation also fixes the unphysical asymmetric Rabi splitting observed in previous semiclassical RT-NEO-TDDFT simulations of vibrational polaritons even for small Rabi splitting, instead yielding a stable, symmetric Rabi splitting. For the intramolecular proton transfer in malonaldehyde, both RT-NEO-Ehrenfest dynamics and its BO counterpart can describe proton delocalization during the real-time nuclear quantum dynamics. Thus, the BO RT-NEO approach provides the foundation for a wide range of chemical and biological applications.