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An accurate assessment of how quantum computers can be used for chemical simulation, especially their potential computational advantages, provides important context on how to deploy these future devices. To perform this assessment reliably, quantum resource estimates must be coupled with classical computations attempting to answer relevant chemical questions and to define the classical algorithms simulation frontier. Herein, we explore the quantum computation and classical computation resources required to assess the electronic structure of cytochrome P450 enzymes (CYPs) and thus define a classical-quantum advantage boundary. This is accomplished by analyzing the convergence of density matrix renormalization group plus n-electron valence state perturbation theory (DMRG+NEVPT2) and coupled-cluster singles doubles with noniterative triples [CCSD(T)] calculations for spin gaps in models of the CYP catalytic cycle that indicate multireference character. The quantum resources required to perform phase estimation using qubitized quantum walks are calculated for the same systems. Compilation into the surface code provides runtime estimates to compare directly to DMRG runtimes and to evaluate potential quantum advantage. Both classical and quantum resource estimates suggest that simulation of CYP models at scales large enough to balance dynamic and multiconfigurational electron correlation has the potential to be a quantum advantage problem and emphasizes the important interplay between classical computations and quantum algorithms development for chemical simulation.

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Reinforcement machine learning is implemented to survey a series of model potential energy surfaces and ultimately identify the global minima point. Through sophisticated reward function design, the introduction of an optimizing target, and incorporating physically motivated actions, the reinforcement learning agent is capable of demonstrating advanced decision making. These improved actions allow the agent to successfully converge to an optimal solution more rapidly when compared to an agent trained without the aforementioned modifications. This study showcases the conceptual feasibility of using reinforcement machine learning to solve difficult environments, namely, potential energy surfaces, with multiple, seemingly, correct solutions in the form of local minima regions. Through these results, we hope to encourage extending reinforcement learning to more complicated optimization problems and using these novel techniques to efficiently solve traditionally challenging problems in chemistry.

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The SmO+ bond energy has been measured by monitoring the threshold for photodissociation of the cryogenically cooled ion. The action spectrum features a very sharp onset, indicating a bond energy of 5.596 ± 0.004 eV. This value, when combined with the literature value of the samarium ionization energy, indicates that the chemi-ionization reaction of atomic Sm with atomic oxygen is endothermic by 0.048 ± 0.004 eV, which has important implications on the reactivity of Sm atoms released into the upper atmosphere. The SmO+ ion was prepared by electrospray ionization followed by collisional breakup of two different precursors and characterized by the vibrational spectrum of the He-tagged ion. The UV photodissociation threshold is similar for the 10 K bare ion and the He tagged ion, which rules out the possible role of metastable electronically excited states. Reanalysis and remeasurement of previous reaction kinetics experiments that are dependent on D0(SmO+) are included, bringing all experimental results in accord.

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Selected configuration interaction (sCI) methods exploit the sparsity of the full configuration interaction (FCI) wave function, yielding significant computational savings and wave function compression without sacrificing the accuracy. Despite recent advances in sCI methods, the selection of important determinants remains an open problem. We explore the possibility of utilizing reinforcement learning approaches to solve the sCI problem. By mapping the configuration interaction problem onto a sequential decision-making process, the agent learns on-the-fly which determinants to include and which to ignore, yielding a compressed wave function at near-FCI accuracy. This method, which we call reinforcement-learned configuration interaction, adds another weapon to the sCI arsenal and highlights how reinforcement learning approaches can potentially help solve challenging problems in electronic structure theory.

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The essential role of a well-defined hydrogen-bond network in achieving chemically reversible multiproton translocations triggered by one-electron electrochemical oxidation/reduction is investigated by using pyridylbenzimidazole-phenol models. The two molecular architectures designed for these studies differ with respect to the position of the N atom on the pyridyl ring. In one of the structures, a hydrogen-bond network extends uninterrupted across the molecule from the phenol to the pyridyl group. Experimental and theoretical evidence indicates that an overall chemically reversible two-proton-coupled electron-transfer process (E2PT) takes place upon electrochemical oxidation of the phenol. This E2PT process yields the pyridinium cation and is observed regardless of the cyclic voltammogram scan rate. In contrast, when the hydrogen-bond network is disrupted, as seen in the isomer, at high scan rates (∼1000 mV s-1) a chemically reversible process is observed with an E1/2 characteristic of a one-proton-coupled electron-transfer process (E1PT). At slow cyclic voltammetric scan rates (<1000 mV s-1) oxidation of the phenol results in an overall chemically irreversible two-proton-coupled electron-transfer process in which the second proton-transfer step yields the pyridinium cation detected by infrared spectroelectrochemistry. In this case, we postulate an initial intramolecular proton-coupled electron-transfer step yielding the E1PT product followed by a slow, likely intermolecular chemical step involving a second proton transfer to give the E2PT product. Insights into the electrochemical behavior of these systems are provided by theoretical calculations of the electrostatic potentials and electric fields at the site of the transferring protons for the forward and reverse processes. This work addresses a fundamental design principle for constructing molecular wires where protons are translocated over varied distances by a Grotthuss-type mechanism.

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Blue light using flavin (BLUF) photoreceptor proteins are critical for many light-activated biological processes and are promising candidates for optogenetics because of their modular nature and long-range signaling capabilities. Although the photocycle of the Slr1694 BLUF domain has been characterized experimentally, the identity of the light-adapted state following photoexcitation of the bound flavin remains elusive. Herein hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations of this photocycle provide a nonequilibrium dynamical picture of a possible mechanism for the formation of the light-adapted state. Photoexcitation of the flavin induces a forward proton-coupled electron transfer (PCET) process that leads to the formation of an imidic acid tautomer of Gln50. The calculations herein show that the subsequent rotation of Gln50 allows a reverse PCET process that retains this tautomeric form. In the resulting purported light-adapted state, the glutamine tautomer forms a hydrogen bond with the flavin carbonyl group. Additional ensemble-averaged QM/MM calculations of the dark-adapted and purported light-adapted states demonstrate that the light-adapted state with the imidic acid glutamine tautomer reproduces the experimentally observed spectroscopic signatures. Specifically, the calculations reproduce the red shifts in the flavin electronic absorption and carbonyl stretch infrared spectra in the light-adapted state. Further hydrogen-bonding analyses suggest the formation of hydrogen-bonding interactions between the flavin and Arg65 in the light-adapted state, providing a plausible explanation for the experimental observation of faster photoinduced PCET in this state. These characteristics of the light-adapted state may also be essential for the long-range signaling capabilities of this photoreceptor protein.

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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.

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Designing molecular platforms for controlling proton and electron movement in artificial photosynthetic systems is crucial to efficient catalysis and solar energy conversion. The transfer of both protons and electrons during a reaction is known as proton-coupled electron transfer (PCET) and is used by nature in myriad ways to provide low overpotential pathways for redox reactions and redox leveling, as well as to generate bioenergetic proton currents. Herein, we describe theoretical and electrochemical studies of a series of bioinspired benzimidazole-phenol (BIP) derivatives and a series of dibenzimidazole-phenol (BI2P) analogs with each series bearing the same set of terminal proton-accepting (TPA) groups. The set of TPAs spans more than 6 pK a units. These compounds have been designed to explore the role of the bridging benzimidazole(s) in a one-electron oxidation process coupled to intramolecular proton translocation across either two (the BIP series) or three (the BI2P series) acid/base sites. These molecular constructs feature an electrochemically active phenol connected to the TPA group through a benzimidazole-based bridge, which together with the phenol and TPA group form a covalent framework supporting a Grotthuss-type hydrogen-bonded network. Infrared spectroelectrochemistry demonstrates that upon oxidation of the phenol, protons translocate across this well-defined hydrogen-bonded network to a TPA group. The experimental data show the benzimidazole bridges are non-innocent participants in the PCET process in that the addition of each benzimidazole unit lowers the redox potential of the phenoxyl radical/phenol couple by 60 mV, regardless of the nature of the TPA group. Using a series of hypothetical thermodynamic steps, density functional theory calculations correctly predicted the dependence of the redox potential of the phenoxyl radical/phenol couple on the nature of the final protonated species and provided insight into the thermodynamic role of dibenzimidazole units in the PCET process. This information is crucial for developing molecular "dry proton wires" with these moieties, which can transfer protons via a Grotthuss-type mechanism over long distances without the intervention of water molecules.

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Blue-light using flavin (BLUF) photoreceptor proteins are essential to many biological processes and are attractive candidates for use in optogenetics. To understand the photocycle mechanism in the Slr1694 BLUF photoreceptor, adiabatic excited-state quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations are performed using Tamm-Dancoff time-dependent density functional theory. These simulations elucidate the roles of protein dynamics, conformational changes, and electrostatics. After photoexcitation to a locally excited state of the flavin, protein reorganization drives electron transfer from Tyr8 to the flavin. The movement of certain charged residues and a decrease in the distance between Tyr8 and the flavin are found to play important roles in facilitating this charge transfer. The formation of this charge-transfer state drives sequential double proton transfer: Tyr8 transfers a proton to the intervening Gln50, which then relays a second proton to the flavin. Although the second proton transfer involves the formation of a singlet diradical ground state, which requires multireference methods, the photocycle dynamics can be continued in an approximate manner by switching to a spin-flip approach. The resulting trajectories trace out the mechanism of photoinduced proton-coupled electron transfer (PCET) in the Slr1694 BLUF photocycle. Propagating the trajectories beyond the PCET reaction identifies possible pathways involving different tautomers of Gln50 that will eventually lead to the light-adapted state. These simulations provide insights into the nonequilibrium dynamics of photoinduced PCET in the Slr1694 BLUF photocycle that have not been attainable with previous simulations.

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Proton-coupled electron transfer (PCET) combines the movement of fundamental charged species to form an essential link between electron- and proton-transport reactions in bioenergetics and catalysis in general. The length scale over which proton transport may occur within PCET processes and the thermodynamic consequences of the resulting proton chemical potential to the oxidation reaction driving these PCET processes have not been generally established. Here we report the design of bioinspired molecules that employ oxidation-reduction processes to move reversibly two, three, and four protons via a Grotthuss-type mechanism along hydrogen-bonded networks up to ∼16 Šin length. These molecules are composed of benzimidazole moieties linking a phenol to the final proton acceptor, a cyclohexylimine. Following electrochemical oxidation of the phenol, the appearance of an infrared band at 1660 cm-1 signals proton arrival at the terminal basic site. Switching the electrode potential to reducing conditions reverses the proton translocation and resets the structure to the initial species. In addition to mimicking the first step of the iconic PCET process used by the Tyrz-His190 redox relay in photosystem II to oxidize water, this work specifically addresses theoretically and experimentally the length scale over which PCET processes may occur. The thermodynamic findings from these redox-driven, bioinspired "proton wires" have implications for understanding and rationally designing pumps for the generation of proton-motive force in artificial and reengineered photosynthesis, as well as for management of proton activity around catalytic sites, including those for water oxidation and oxygen reduction.

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Photoreceptor proteins control vital cellular responses to light. The photocycle of the Slr1694 blue light using flavin photoreceptor is initiated by photoexcitation to a locally excited state within the flavin, followed by electron transfer from Tyr8 to the flavin and a proton relay from Tyr8 to the flavin via an intervening glutamine. Herein, the two-dimensional excited state potential energy surfaces associated with this double proton-transfer reaction are computed using the complete active space self-consistent-field method and multiconfigurational perturbation theory, including the protein and solvent environment with electrostatic embedding. The double proton-transfer reaction was found to be energetically unfavorable in the ground state and locally excited state but energetically favorable in the charge-transfer state corresponding to electron transfer from Tyr8 to the flavin. These results indicate that the proton-coupled electron transfer process is sequential, with electron transfer preceding double proton transfer, and that the double proton-transfer reaction is also sequential, with proton transfer from Tyr8 to Gln50 followed by proton transfer from Gln50 to the flavin. The barrier is lower for the first proton-transfer reaction, and both barriers are significantly influenced by geometrical changes within the active site, particularly the proton donor-acceptor distance as well as the protein environment. These calculations provide insight into the impact of protein reorganization and electrostatics on the excited electronic states prior to and during the double proton-transfer reaction. This interplay between excited states and the environment has implications for other photoreceptor proteins.

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Bioinspired constructs consisting of benzimidazole-phenol moieties bearing N-phenylimines as proton-accepting substituents have been designed to mimic the H-bond network associated with the TyrZ-His190 redox relay in photosystem II. These compounds provide a platform to theoretically and experimentally explore and expand proton-coupled electron transfer (PCET) processes. The models feature H-bonds between the phenol and the nitrogen at the 3-position of the benzimidazole and between the 1 H-benzimidazole proton and the imine nitrogen. Protonation of the benzimidazole and the imine can be unambiguously detected by infrared spectroelectrochemistry (IRSEC) upon oxidation of the phenol. DFT calculations and IRSEC results demonstrate that with sufficiently strong electron-donating groups at the para-position of the N-phenylimine group (e.g., -OCH3 substitution), proton transfer to the imine is exergonic upon phenol oxidation, leading to a one-electron, two-proton (E2PT) product with the imidazole acting as a proton relay. When transfer of the second proton is not sufficiently exergonic (e.g., -CN substitution), a one-electron, one-proton transfer (EPT) product is dominant. Thus, the extent of proton translocation along the H-bond network, either ∼1.6 Å or ∼6.4 Å, can be controlled through imine substitution. Moreover, the H-bond strength between the benzimidazole NH and the imine nitrogen, which is a function of their relative p Ka values, and the redox potential of the phenoxyl radical/phenol couple are linearly correlated with the Hammett constants of the substituents. In all cases, a high potential (∼1 V vs SCE) is observed for the phenoxyl radical/phenol couple. Designing and tuning redox-coupled proton wires is important for understanding bioenergetics and developing novel artificial photosynthetic systems.

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Photoreceptor proteins play a vital role in a wide range of light-regulated processes. The formation of the light-adapted state of blue light using flavin (BLUF) photoreceptors is thought to involve rearrangements of hydrogen-bonding networks upon photoexcitation. Free energy simulations with partial charges corresponding to relevant ground and excited states of the Slr1694 BLUF domain characterize conformations prior to and following photoexcitation. The simulations indicate that Trp91 is thermodynamically favored to be in the active site, although it is also able to sample conformations outside the active site. For experimentally observed conformations of Trp91, Gln50 is thermodynamically favored to be oriented for a proton relay bridging Tyr8 and the flavin. When Trp91 is rotated such that it can donate a hydrogen bond to Gln50, as observed in other BLUF domains, the proton relay is not thermodynamically favored in the ground state, providing a possible explanation for the relatively fast photocycle of the Slr1694 BLUF domain. Photoexcitation to the locally excited (LE) state of the flavin induces the formation of the proton relay if it is not already formed. Electrostatically embedded time-dependent density functional theory calculations indicate that the proton relay reduces the energy gap between the LE state and the charge-transfer (CT) state associated with electron transfer from Tyr8 to the flavin. Although the CT state is higher in energy than the LE state prior to photoexcitation, the protein environment can reorganize in a manner that stabilizes the CT state so that it is lower than the LE state, enabling the LE to CT state transition. An electrostatic analysis identifies motions of individual residues, such as Arg65, that stabilize electron transfer from Tyr8 to the flavin. These conformational changes facilitate the critical proton-coupled electron transfer reaction in the BLUF photocycle.

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We previously demonstrated that we can image electronic excitations of quantum dots by single-molecule absorption scanning tunneling microscopy (SMA-STM). With this technique, a modulated laser beam periodically saturates an electronic transition of a single nanoparticle, and the resulting tunneling current modulation ΔI(x0, y0) maps out the SMA-STM image. In this paper, we first derive the basic theory to calculate ΔI(x0, y0) in the one-electron approximation. For near-resonant tunneling through an empty orbital "i" of the nanostructure, the SMA-STM signal is approximately proportional to the electron density φix0,y02 of the excited orbital in the tunneling region. Thus, the SMA-STM signal is approximated by an orbital density map (ODM) of the resonantly excited orbital at energy Ei. The situation is more complex for correlated electron motion, but either way a slice through the excited electronic state structure in the tunneling region is imaged. We then show experimentally that we can nudge quantum dots on the surface and roll them, thus imaging excited state electronic structure of a single quantum dot at different orientations. We use density functional theory to model ODMs at various orientations, for qualitative comparison with the SMA-STM experiment. The model demonstrates that our experimentally observed signal monitors excited states, localized by defects near the surface of an individual quantum dot. The sub-nanometer super-resolution imaging technique demonstrated here could become useful for mapping out the three-dimensional structure of excited states localized by defects within nanomaterials.

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We present a linear response formalism for the description of the electronic excitations of a noncollinear reference defined via Kohn-Sham spin density functional methods. A set of auxiliary variables, defined using the density and noncollinear magnetization density vector, allows the generalization of spin density functional kernels commonly used in collinear DFT to noncollinear cases, including local density, GGA, meta-GGA and hybrid functionals. Working equations and derivations of functional second derivatives with respect to the noncollinear density, required in the linear response noncollinear TDDFT formalism, are presented in this work. This formalism takes all components of the spin magnetization into account independent of the type of reference state (open or closed shell). As a result, the method introduced here is able to afford a nonzero local xc torque on the spin magnetization while still satisfying the zero-torque theorem globally. The formalism is applied to a few test cases using the variational exact-two-component reference including spin-orbit coupling to illustrate the capabilities of the method.

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We explore the question of whether mean-field or "Ehrenfest" mixed quantum-classical dynamics is capable of capturing the quantized vibrational features in photoabsorption spectra that result from infrared and Raman-active vibrational transitions. We show that vibrational and electronic absorption spectra can indeed be obtained together within a single Ehrenfest simulation. Furthermore, the electronic transitions show new sidebands that are absent in electronic dynamics simulations with fixed nuclei. Inspection of the electronic sidebands reveals that the spacing corresponds to vibrational frequencies of totally symmetric vibrational modes of the ground electronic state. A simple derivation of the time-evolving dipole in the presence of external fields and vibrational motion shows the origin of these features, demonstrating that mixed quantum-classical Ehrenfest dynamics is capable of producing infrared, Raman, and electronic absorption spectra from a single simulation.

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Solutions of the real-time time-dependent density functional theory (RT-TDDFT) equations provide an affordable route to understanding the electronic dynamics that underpins many spectroscopic techniques. From the solutions of the RT-TDDFT equations, it is possible to extract optical absorption and circular dichroism spectra, as well as descriptions of charge transfer and charge transport dynamics. In order to apply RT-TDDFT to increasingly large systems, it is necessary to develop methods to overcome computational bottlenecks. One current bottleneck is the [Formula: see text] cost required to form the time propagator for the RT-TDDFT equations, because of the full matrix diagonalization that is required at each time step. Here, we present a (semi)diagonalization-free formation of the propagator based on a nonrecursive Chebyshev polynomial expansion. The Chebyshev expansion relies only on matrix multiply operations which have lower computational cost and are furthermore extremely parallelizable. We demonstrate the accuracy and stability of the Chebyshev approach, and then discuss the favorable scaling of the method, compared to traditional approaches based on matrix diagonalization. The Chebyshev expansion method should enable the application of RT-TDDFT methods to large systems such as nanocrystals and biomolecules.

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We report the development of a real time propagation method for solving the time-dependent relativistic exact two-component density functional theory equations (RT-X2C-TDDFT). The method is fundamentally non-perturbative and may be employed to study nonlinear responses for heavy elements which require a relativistic Hamiltonian. We apply the method to several group 12 atoms as well as heavy-element hydrides, comparing with the extensive theoretical and experimental studies on this system, which demonstrates the correctness of our approach. Because the exact two-component Hamiltonian contains spin-orbit operators, the method is able to describe the non-zero transition moment of otherwise spin-forbidden processes in non-relativistic theory. Furthermore, the two-component approach is more cost effective than the full four-component approach, with similar accuracy. The RT-X2C-TDDFT will be useful in future studies of systems containing heavy elements interacting with strong external fields.

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In this work, we present a linear-response formalism of the complex two-component Hartree-Fock Hamiltonian that includes relativistic effects within the Douglas-Kroll-Hess and the Exact-Two-Component frameworks. The method includes both scalar and spin relativistic effects in the variational description of electronic ground and excited states, although it neglects the picture-change and explicit spin-orbit contributions arising from the two-electron interaction. An efficient direct formalism of solving the complex two-component response function is also presented in this work. The presence of spin-orbit couplings in the Hamiltonian and the two-component nature of the wave function and Fock operator allows the computation of excited-state zero-field splittings of systems for which relativistic effects are dominated by the one-electron term. Calculated results are compared to experimental reference values to assess the quality of the underlying approximations. The results show that the relativistic two-component linear response methods are able to capture the excited-state zero-field splittings with good agreement with experiments for the systems considered here, with all approximations exhibiting a similar performance. However, the error increases for heavy elements and for states of high orbital angular momentum, suggesting the importance of the two-electron relativistic effect in such situations.