Abstract:The
quantum mechanical treatment of both electrons and nuclei is
crucial in nonadiabatic dynamical processes such as proton-coupled
electron transfer. The nuclear−electronic orbital (NEO) method
provides an elegant framework for including nuclear quantum effects
beyond the Born–Oppenheimer approximation. To enable the study
of nonequilibrium properties, we derive and implement a real-time
NEO (RT-NEO) approach based on time-dependent Hatree-Fock or density
functional theory, in which the electronic and nuclear… Show more
“…This approach also neglects the nuclear quantum effects of the transferring protons. Alternative strategies using real-time time-dependent density functional theory 42 and its extension within the nuclear-electronic orbital (NEO) framework 43 to treat the transferring protons quantum mechanically, possibly on systems including the photosensitizer, would address these issues but are not yet applicable to these types of systems. Moreover, the times computed for proton transfer are not directly comparable to putative solution-phase experiments because the calculations are performed in the gas phase.…”
The coupling between electrons and protons and the long-range transport of protons play
important roles throughout biology. Biomimetic systems derived from benzimidazole-phenol
(BIP) constructs have been designed to undergo proton-coupled electron transfer (PCET)
upon electrochemical or photochemical oxidation. Moreover, these systems can transport
protons along hydrogen-bonded networks or proton wires through multiproton PCET. Herein,
the nonequilibrium dynamics of both single and double proton transfer in BIP molecules
initiated by oxidation are investigated with first-principles molecular dynamics
simulations. Although these processes are concerted in that no thermodynamically stable
intermediate is observed, the simulations predict that they are predominantly
asynchronous on the ultrafast time scale. For both systems, the first proton transfer
typically occurs ∼100 fs after electron transfer. For the double proton transfer
system, typically the second proton transfer occurs hundreds of femtoseconds after the
initial proton transfer. A machine learning algorithm was used to identify the key
molecular vibrational modes essential for proton transfer: a slow, in-plane bending mode
that dominates the overall inner-sphere reorganization, the proton donor–acceptor
motion that leads to vibrational coherence, and the faster donor–hydrogen
stretching mode. The asynchronous double proton transfer mechanism can be understood in
terms of a significant mode corresponding to the two anticorrelated proton
donor–acceptor motions, typically decreasing only one donor–acceptor
distance at a time. Although these PCET processes appear concerted on the time scale of
typical electrochemical experiments, attaching these BIP constructs to photosensitizers
may enable the detection of the asynchronicity of the electron and multiple proton
transfers with ultrafast two-dimensional spectroscopy. Understanding the fundamental
PCET mechanisms at this level will guide the design of PCET systems for catalysis and
energy conversion processes.
“…This approach also neglects the nuclear quantum effects of the transferring protons. Alternative strategies using real-time time-dependent density functional theory 42 and its extension within the nuclear-electronic orbital (NEO) framework 43 to treat the transferring protons quantum mechanically, possibly on systems including the photosensitizer, would address these issues but are not yet applicable to these types of systems. Moreover, the times computed for proton transfer are not directly comparable to putative solution-phase experiments because the calculations are performed in the gas phase.…”
The coupling between electrons and protons and the long-range transport of protons play
important roles throughout biology. Biomimetic systems derived from benzimidazole-phenol
(BIP) constructs have been designed to undergo proton-coupled electron transfer (PCET)
upon electrochemical or photochemical oxidation. Moreover, these systems can transport
protons along hydrogen-bonded networks or proton wires through multiproton PCET. Herein,
the nonequilibrium dynamics of both single and double proton transfer in BIP molecules
initiated by oxidation are investigated with first-principles molecular dynamics
simulations. Although these processes are concerted in that no thermodynamically stable
intermediate is observed, the simulations predict that they are predominantly
asynchronous on the ultrafast time scale. For both systems, the first proton transfer
typically occurs ∼100 fs after electron transfer. For the double proton transfer
system, typically the second proton transfer occurs hundreds of femtoseconds after the
initial proton transfer. A machine learning algorithm was used to identify the key
molecular vibrational modes essential for proton transfer: a slow, in-plane bending mode
that dominates the overall inner-sphere reorganization, the proton donor–acceptor
motion that leads to vibrational coherence, and the faster donor–hydrogen
stretching mode. The asynchronous double proton transfer mechanism can be understood in
terms of a significant mode corresponding to the two anticorrelated proton
donor–acceptor motions, typically decreasing only one donor–acceptor
distance at a time. Although these PCET processes appear concerted on the time scale of
typical electrochemical experiments, attaching these BIP constructs to photosensitizers
may enable the detection of the asynchronicity of the electron and multiple proton
transfers with ultrafast two-dimensional spectroscopy. Understanding the fundamental
PCET mechanisms at this level will guide the design of PCET systems for catalysis and
energy conversion processes.
“…Figure 4Excited-state intramolecular proton transfer in the oHBA molecule, where the transferring proton is treated quantum-mechanically on the same level as the electrons within the NEO framework. Adapted with permission from [38]. (Online version in colour.)…”
The Born–Oppenheimer approximation, which assumes that the electrons respond instantaneously to the motion of the nuclei, breaks down for a wide range of chemical and biological processes. The rate constants of such nonadiabatic processes can be calculated using analytical theories, and the real-time nonequilibrium dynamics can be described using numerical atomistic simulations. The selection of an approach depends on the desired balance between accuracy and efficiency. The computational expense of generating potential energy surfaces on-the-fly often favours the use of approximate, robust and efficient methods such as trajectory surface hopping for large, complex systems. The development of formally exact non-Born–Oppenheimer methods and the exploration of well-defined approximations to such methods are critical for providing benchmarks and preparing for the next generation of faster computers. Thus, the parallel development of rigorous but computationally expensive methods and more approximate but computationally efficient methods is optimal. This Perspective briefly summarizes the available theoretical and computational non-Born–Oppenheimer methods and presents examples illustrating how analytical theories and nonadiabatic dynamics simulations can elucidate the fundamental principles of chemical and biological processes. These examples also highlight how theoretical calculations are able to guide the interpretation of experimental data and provide experimentally testable predictions for nonadiabatic processes.
This article is part of the theme issue ‘Chemistry without the Born–Oppenheimer approximation’.
“…This rather ingenious treatment allows the full machinery of electronic structure theory to be applied, natively accounting for electron and nuclear dynamics. Some of the methods already reported include HF, 24,25 many-body perturbation theory, [28][29][30] Configuration Interaction (CI), [31][32][33] density-matrix renormalization group, 34 multi-configuration self-consistent-field, 25 coupled cluster, 28,35,36 time dependent HF 37 and some explicitly correlated variants. [38][39][40] This framework cannot, however, be applied to the whole molecular system in a general manner.…”
We introduce a new theoretical and computational framework for treating molecular quantum mechanics without the Born-Oppenheimer approximation. The molecular wavefunction is represented in a tensor-product space of electronic and vibrational basis functions, with electronic basis chosen to reproduce the mean-field electronic structure at all geometries. We show how to transform the Hamiltonian to a fully second quantized form with creation/annihilation operators for electronic and vibrational quantum particles; paving the way for polynomial-scaling approximations to the tensor-product space formalism. In addition, we make a proof-of-principle application of the new ansatz to the vibronic spectrum of C 2 .
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