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We present a Lagrangian-based implementation of Ehrenfest dynamics with nuclear-electronic orbital (NEO) theory and real-time time-dependent density functional theory for extended periodic systems. In addition to a quantum dynamical treatment of electrons and selected protons, this approach allows for the classical movement of all other nuclei to be taken into account in simulations of condensed matter systems. Furthermore, we introduce a Lagrangian formulation for the traveling proton basis approach and propose new schemes to enhance its application for extended periodic systems. Validation and proof-of-principle applications are performed on electronically excited proton transfer in the o-hydroxybenzaldehyde molecule with explicit solvating water molecules. These simulations demonstrate the importance of solvation dynamics and a quantum treatment of transferring protons. This work broadens the applicability of the NEO Ehrenfest dynamics approach for studying complex heterogeneous systems in the condensed phase., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

The enzyme ribonucleotide reductase plays a critical role in DNA synthesis and repair. Its mechanism requires long-range radical transfer through a series of proton-coupled electron transfer (PCET) steps. Nuclear quantum effects such as zero-point energy, proton delocalization, and hydrogen tunneling are known to be important in PCET. We present a strategy for efficiently incorporating nuclear quantum effects into multidimensional free energy surfaces and real-time dynamical simulations for condensed-phase systems such as enzymes. This strategy is based on the nuclear-electronic orbital (NEO) method, which treats specified protons quantum mechanically on the same level as the electrons. NEO density functional theory (NEO-DFT) is combined with the quantum mechanical/molecular mechanical finite temperature string method with umbrella sampling via a simple reweighting procedure. Application of this strategy to PCET between two tyrosines, Y731 and Y730, in ribonucleotide reductase illustrates that nuclear quantum effects could either raise or lower the free energy barrier, leading to a range of possible kinetic isotope effects. Real-time time-dependent DFT (RT-NEO-TDDFT) simulations highlight nuclear-electronic quantum dynamics. These approaches enable the incorporation of nuclear quantum effects into a wide range of chemically and biologically important processes.

Bioinspired benzimidazole-phenol constructs with an intramolecular hydrogen bond connecting the phenol and the benzimidazole have been synthesized to study both proton-coupled electron transfer (PCET) and excited-state intramolecular proton transfer (ESIPT) processes. Strategic incorporation of a methyl group disrupts the coplanarity between the aromatic units, causing a pronounced twist, weakening the intramolecular hydrogen bond, decreasing the phenol redox potential, reducing the chemical reversibility, and quenching the fluorescence emission. Infrared spectroelectrochemistry and transient absorption spectroscopy confirm the formation of the oxidized product upon PCET and probe excited-state relaxation mechanisms, respectively. Density functional theory calculations of redox potentials corroborate the experimental findings. Additionally, time-dependent density functional theory calculations uncover the fluorescence quenching mechanism, showing that the nonradiative twisted intramolecular charge transfer state responsible for fluorescence quenching is more energetically favorable in the methyl-substituted system. Incorporating groups causing steric hindrance expands the design of biomimetic systems capable of performing both PCET and ESIPT.

A bioinspired naphthoquinone model of the quinones in photosynthetic reaction centers but bearing an intramolecular hydrogen-bonded carboxylic acid has been synthesized and characterized electrochemically, spectroscopically, and computationally to provide mechanistic insight into the role of proton-coupled electron transfer (PCET) of quinone reduction in photosynthesis. The reduction potential of this construct is 370 mV more positive than the unsubstituted naphthoquinone. In addition to the reversible cyclic voltammetry, infrared spectroelectrochemistry confirms that the naphthoquinone/naphthoquinone radical anion couple is fully reversible. Calculated redox potentials agree with the experimental trends arising from the intramolecular hydrogen bond. Molecular electrostatic potentials illustrate the reversible proton transfer driving forces, and analysis of the computed vibrational spectra supports the possibility of a combination of electron transfer and PCET processes. The significance of PCET, reversibility, and redox potential management relevant to the design of artificial photosynthetic assemblies involving PCET processes is discussed., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

Proton transfer and hydrogen tunneling play key roles in many processes of chemical and biological importance. The generalized nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method was developed in order to capture hydrogen tunneling effects in systems involving the transfer and tunneling of one or more protons. The generalized NEO-MSDFT method treats the transferring protons quantum mechanically on the same level as the electrons and obtains the delocalized vibronic states associated with hydrogen tunneling by mixing localized NEO-DFT states in a nonorthogonal configuration interaction scheme. Herein, we present the derivation and implementation of analytical gradients for the generalized NEO-MSDFT vibronic state energies and the nonadiabatic coupling vectors between these vibronic states. We use this methodology to perform adiabatic and nonadiabatic dynamics simulations of the double proton transfer reactions in the formic acid dimer and the heterodimer of formamidine and formic acid. The generalized NEO-MSDFT method is shown to capture the strongly coupled synchronous or asynchronous tunneling of the two protons in these processes. Inclusion of vibronically nonadiabatic effects is found to significantly impact the double proton transfer dynamics. This work lays the foundation for a variety of nonadiabatic dynamics simulations of multiple proton transfer systems, such as proton relays and hydrogen-bonding networks.

Experimental methods capable of selectively probing water at the DNA minor groove, major groove, and phosphate backbone are crucial for understanding how hydration influences DNA structure and function. Chiral-selective sum frequency generation spectroscopy (chiral SFG) is unique among vibrational spectroscopies because it can selectively probe water molecules that form chiral hydration structures around biomolecules. However, interpreting chiral SFG spectra is challenging since both water and the biomolecule can produce chiral SFG signals. Here, we combine experiment and computation to establish a theoretical framework for the rigorous interpretation of chiral SFG spectra of DNA. We demonstrate that chiral SFG detects the N-H stretch of DNA base pairs and the O-H stretch of water, exclusively probing water molecules in the DNA first hydration shell. Our analysis reveals that DNA transfers chirality to water molecules only within the first hydration shell, so they can be probed by chiral SFG spectroscopy. Beyond the first hydration shell, the electric field-induced water structure is symmetric and, therefore, precludes chiral SFG response. Furthermore, we find that chiral SFG can differentiate chiral subpopulations of first hydration shell water molecules at the minor groove, major groove, and phosphate backbone. Our findings challenge the scientific perspective dominant for more than 40 years that the minor groove "spine of hydration" is the only chiral water structure surrounding the DNA double helix. By identifying the molecular origins of the DNA chiral SFG spectrum, we lay a robust experimental and theoretical foundation for applying chiral SFG to explore the chemical and biological physics of DNA hydration., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

A microscopic understanding of electric fields and molecular polarization at interfaces will aid in the design of electrocatalytic systems. Herein, variants of 4-mercaptobenzonitrile are designed to test different schemes for breaking the continuous conjugation between a gold electrode surface and a nitrile group. Periodic density functional theory calculations predict applied potential dependencies of the CN vibrational frequencies similar to those observed experimentally. The CN frequency response decreased more when the conjugation was broken between the benzene ring and the nitrile group than between the electrode and the benzene ring, highlighting molecular polarizability effects. The systems with continuous or broken conjugation are dominated by electro-inductive effects or through-space electrostatic effects, respectively. Analysis of the fractional charge transfer between the electrode and the molecule as well as the occupancy of the CN antibonding orbital provides further insights. Balancing the effects of molecular polarizability, electro-induction, and through-space electrostatics has broad implications for electrocatalyst design.

Redox-active residues, such as tyrosine and tryptophan, play important roles in a wide range of biological processes. The α 3 Y de novo protein, which is composed of three α helices and a tyrosine residue Y32, provides a platform for investigating the redox properties of tyrosine in a well-defined protein environment. Herein, the proton-coupled electron transfer (PCET) reaction that occurs upon oxidation of tyrosine in this model protein by a ruthenium photosensitizer is studied by using a vibronically nonadiabatic PCET theory that includes hydrogen tunneling and excited vibronic states. The input quantities to the analytical nonadiabatic rate constant expression, such as the diabatic proton potential energy curves and associated proton vibrational wave functions, reorganization energy, and proton donor-acceptor distribution functions, are obtained from density functional theory calculations on model systems and molecular dynamics simulations of the solvated α 3 Y protein. Two possible proton acceptors, namely, water or a glutamate residue in the protein scaffold, are explored. The PCET rate constant is greater when glutamate is the proton acceptor, mainly due to the more favorable driving force and shorter equilibrium proton donor-acceptor distance, although contributions from excited vibronic states mitigate these effects. Nevertheless, water could be the dominant proton acceptor if its equilibrium constant associated with hydrogen bond formation is significantly greater than that for glutamate. Although these calculations do not definitively identify the proton acceptor for this PCET reaction, they elucidate the conditions under which each proton acceptor can be favored. These insights have implications for tyrosine-based PCET in a wide variety of biochemical processes.

Controlling reactivity with electric fields is a persistent challenge in chemistry. One approach is to tether ions at well-defined locations near a reactive center. To quantify fields arising from ions, we report crown ethers that capture metal cations as field sources and a covalently bound vibrational Stark shift probe as a field sensor. We use experiments and computations in both the gas and liquid phases to quantify the vibrational frequencies of the probe and estimate the electric fields from the captured ions. Cations, in general, blue shift the probe frequency, with effective fields estimated to vary in the range of ∼0.2-3 V/nm in the liquid phase. Comparison of the gas and liquid phase data provides insight into the effects of mutual polarization of the molecule and solvent and screening of the ion's field. These findings reveal the roles of charge, local screening, and geometry in the design of tailored electric fields.

Immobilized cobalt phthalocyanine (CoPc) is a highly promising architecture for the six-proton, six-electron reduction of CO 2 to methanol. This electroreduction process relies on proton-coupled electron transfer (PCET) reactions that can occur by sequential or concerted mechanisms. Immobilization on a conductive support such as carbon nanotubes or graphitic flakes can fundamentally alter the PCET mechanisms. We use density functional theory (DFT) calculations of CoPc adsorbed on an explicit graphitic surface model to investigate intermediates in the electroreduction of CO 2 to methanol. Our calculations show that the alignment of the CoPc and graphitic electronic states influences the reductive chemistry. These calculations also distinguish between charging the graphitic surface and reducing the CoPc and adsorbed intermediates as electrons are added to the system. This analysis allows us to identify the chemical transformations that are likely to be concerted PCET, defined for these systems as the mechanism in which protonation of a CO 2 reduction intermediate is accompanied by electron abstraction from the graphitic surface to the adsorbate without thermodynamically stable intermediates. This work establishes a mechanistic pathway for methanol production that is consistent with experimental observations and provides fundamental insight into how immobilization of the CoPc impacts its CO 2 reduction chemistry.

In the recently discovered proton-coupled energy transfer (PCEnT) mechanism, the transfer of electronic excitation energy between donor and acceptor chromophores is coupled to a proton transfer reaction. Herein, we develop a general theory for PCEnT and derive an analytical expression for the nonadiabatic PCEnT rate constant. This theory treats the transferring hydrogen nucleus quantum mechanically and describes the PCEnT process in terms of nonadiabatic transitions between reactant and product electron-proton vibronic states. The rate constant is expressed as a summation over these vibronic states, and the contribution of each pair of vibronic states depends on the square of the vibronic coupling as well as the spectral convolution integral, which can be viewed as a generalization of the Förster-type spectral overlap integral for vibronic rather than electronic states. The convolution integral also accounts for the common vibrational modes shared by the donor and acceptor chromophores for intramolecular PCEnT. We apply this theory to model systems to investigate the key features of PCEnT processes. The excited vibronic states can contribute significantly to the total PCEnT rate constant, and the common modes can either slow down or speed up the process. Because the pairs of vibronic states that contribute the most to the PCEnT rate constant may correspond to spectroscopically dark states, PCEnT could occur even when there is no apparent overlap between the donor emission and acceptor absorption spectra. This theory will assist in the interpretation of experimental data and will guide the design of additional PCEnT systems., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Combining real-time electronic structure with the nuclear-electronic orbital (NEO) method has enabled the simulation of complex nonadiabatic chemical processes. However, accurate descriptions of hydrogen tunneling and double excitations require multiconfigurational treatments. Herein, we develop and implement the real-time NEO time-dependent configuration interaction (NEO-TDCI) approach. Comparison to NEO-full CI calculations of absorption spectra for a molecular system shows that the NEO-TDCI approach can accurately capture the tunneling splitting associated with the electronic ground state as well as vibronic progressions corresponding to double electron-proton excitations associated with excited electronic states. Both of these features are absent from spectra obtained with single reference real-time NEO methods. Our simulations of hydrogen tunneling dynamics illustrate the oscillation of the proton density from one side to the other via a delocalized, bilobal proton wave function. These results indicate that the NEO-TDCI approach is highly suitable for studying hydrogen tunneling and other inherently multiconfigurational systems.

Colloidal gold nanoparticles (AuNPs) have myriad scientific and technological applications, but their fundamental redox chemistry is underexplored. Reported here are titration studies of oxidation and reduction reactions of aqueous AuNP colloids, which show that the AuNPs bind substantial hydrogen (electrons + protons) under mild conditions. The 5 nm AuNPs are reduced to a similar extent with reductants from borohydrides to H 2 and are reoxidized back essentially to their original state by oxidants, including O 2 . The reactions were monitored via surface plasmon resonance (SPR) optical absorption, which was shown to be much more sensitive to surface H than to changes in solution conditions. Reductions with H 2 occurred without pH changes, demonstrating that hydrogenation forms surface H rather than releasing H + . Computational studies suggested that an SPR blueshift was expected for H atom addition, while just electron addition likely would have caused a redshift. Titrations consistently showed a maximum redox change of the 5 nm NPs, independent of the reagent, corresponding to 9% of the total gold or ∼30% hydrogen surface coverage (∼370 H per AuNP). Larger AuNPs showed smaller maximum fractional surface coverages. We conclude that H binds to the edge, corner, and defect sites of the AuNPs, which explains the stoichiometric limitation and the size effect. The finding of substantial and stable hydrogen on the AuNP surface under mild reducing conditions has potential implications for various applications of AuNPs in reducing environments, from catalysis to biomedicine. This finding contrasts with the behavior of bulk gold and with the typical electron-focused perspective in this field.

Nuclear quantum effects play an important role in the structure and thermodynamics of aqueous systems. By performing a many-body expansion with nuclear-electronic orbital (NEO) theory, we show that proton quantization can give rise to significant energetic contributions for many-body interactions spanning several molecules in single-point energy calculations of water clusters. Although zero-point motion produces a large increase in energy at the one-body level, nuclear quantum effects serve to stabilize higher-order molecular interactions. These results are significant because they demonstrate that nuclear quantum effects play a nontrivial role in many-body interactions of aqueous systems. Our approach also provides a pathway for incorporating nuclear quantum effects into water potential energy surfaces. The NEO approach is advantageous for many-body expansion analyses because it includes nuclear quantum effects directly in the energies.

A Co II -porphyrin complex (1) with an appended aza-crown ether for Lewis acid (LA) binding was synthesized and characterized. NMR spectroscopy and electrochemistry show that cationic group I and II LAs ( i.e. , Li + , Na + , K + , Ca 2+ , Sr 2+ , and Ba 2+ ) bind to the aza-crown ether group of 1. The binding constant for Li + is comparable to that observed for a free aza-crown ether. LA binding causes an anodic shift in the Co II /Co I couple of between 10 and 40 mV and also impacts the Co III /Co II couple. The magnitude of the anodic shift of the Co II /Co I couple varies linearly with the strength of the LA as determined by the p K a of the corresponding metal-aqua complex, with dications giving larger shifts than monocations. The extent of the anodic shift of the Co II /Co I couple also increases as the ionic strength of the solution decreases. This is consistent with electric field effects being responsible for the changes in the redox properties of 1 upon LA binding and provides a novel method to tune the reduction potential. Density functional theory calculations indicate that the bound LA is 5.6 to 6.8 Å away from the Co II ion, demonstrating that long-range electrostatic effects, which do not involve changes to the primary coordination sphere, are responsible for the variations in redox chemistry. Compound 1 was investigated as a CO 2 reduction electrocatalyst and shows high activity but rapid decomposition., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

The enzyme ribonucleotide reductase, which is essential for DNA synthesis, initiates the conversion of ribonucleotides to deoxyribonucleotides via radical transfer over a 32 Å pathway composed of proton-coupled electron transfer (PCET) reactions. Previously, the first three PCET reactions in the α subunit were investigated with hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations. Herein, the fourth PCET reaction in this subunit between C439 and guanosine diphosphate (GDP) is simulated and found to be slightly exoergic with a relatively high free energy barrier. To further elucidate the mechanisms of all four PCET reactions, we analyzed the vibronic and electron-proton nonadiabaticities. This analysis suggests that interfacial PCET between Y356 and Y731 is vibronically and electronically nonadiabatic, whereas PCET between Y731 and Y730 and between C439 and GDP is fully adiabatic and PCET between Y730 and C439 is in the intermediate regime. These insights provide guidance for selecting suitable rate constant expressions for these PCET reactions.

Chirality-selective vibrational sum frequency generation (chiral SFG) spectroscopy has emerged as a powerful technique for the study of biomolecular hydration water due to its sensitivity to the induced chirality of the first hydration shell. Thus far, water O-H vibrational bands in phase-resolved heterodyne chiral SFG spectra have been fit using one Lorentzian function per vibrational band, and the resulting fit has been used to infer the underlying frequency distribution. Here, we show that this approach may not correctly reveal the structure and dynamics of hydration water. Our analysis illustrates that the chiral SFG responses of symmetric and asymmetric O-H stretch modes of water have opposite phase and equal magnitude and are separated in energy by intramolecular vibrational coupling and a heterogeneous environment. The sum of the symmetric and asymmetric responses implies that an O-H stretch in a heterodyne chiral SFG spectrum should appear as two peaks with opposite phase and equal amplitude. Using pairs of Lorentzian functions to fit water O-H stretch vibrational bands, we improve spectral fitting of previously acquired experimental spectra of model β-sheet proteins and reduce the number of free parameters. The fitting allows us to estimate the vibrational frequency distribution and thus reveals the molecular interactions of water in hydration shells of biomolecules directly from chiral SFG spectra., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

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 Au 6 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.

The proton-coupled electron transfer (PCET) reactions of tyrosine (Y) are instrumental to many redox reactions in nature. This study investigates how the local environment and the thermodynamic properties of Y influence its PCET characteristics. Herein, 2- and 4-mercaptophenol (MP) are placed in the well-folded α 3 C protein (forming 2MP-α 3 C and 4MP-α 3 C) and oxidized by external light-generated [Ru(L) 3 ] 3+ complexes. The resulting neutral radicals are long-lived (>100 s) with distinct optical and EPR spectra. Calculated spin-density distributions are similar to canonical Y˙ and display very little spin on the S-S bridge that ligates the MPs to C 32 inside the protein. With 2MP-α 3 C and 4MP-α 3 C we probe how proton transfer (PT) affects the PCET rate constants and mechanisms by varying the degree of solvent exposure or the potential to form an internal hydrogen bond. Solution NMR ensemble structures confirmed our intended design by displaying a major difference in the phenol OH solvent accessible surface area (≤∼2% for 2MP and 30-40% for 4MP). Additionally, 2MP-C 32 is within hydrogen bonding distance to a nearby glutamate (average O-O distance is 3.2 ± 0.5 Å), which is suggested also by quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations. Neither increased exposure of the phenol OH to solvent (buffered water), nor the internal hydrogen bond, was found to significantly affect the PCET rates. However, the lower phenol p K a values associated with the MP-α 3 C proteins compared to α 3 Y provided a sufficient change in PT driving force to alter the PCET mechanism. The PCET mechanism for 2MP-α 3 C and 4MP-α 3 C with moderately strong oxidants was predominantly step-wise PTET for pH values, but changed to concerted PCET at neutral pH values and below when a stronger oxidant was used, as found previously for α 3 Y. This shows how the balance of ET and PT driving forces is critical for controlling PCET mechanisms. The presented results improve our general understanding of amino-acid based PCET in enzymes., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

The proton-coupled electron transfer (PCET) mechanism for the reaction M ox -OH + e - + H + → M red -OH 2 was determined through the kinetic resolution of the independent electron transfer (ET) and proton transfer (PT) steps. The reaction of interest was triggered by visible light excitation of [Ru II (tpy)(bpy')H 2 O] 2+ , Ru II -OH 2 , where tpy is 2,2':6',2″-terpyridine and bpy' is 4,4'-diaminopropylsilatrane-2,2'-bipyridine, anchored to In 2 O 3 :Sn (ITO) thin films in aqueous solutions. Interfacial kinetics for the PCET reduction reaction were quantified by nanosecond transient absorption spectroscopy as a function of solution pH and applied potential. Data acquired at pH = 5-10 revealed a stepwise electron transfer-proton transfer (ET-PT) mechanism, while kinetic measurements made below p K a (Ru III -OH/OH 2 ) = 1.3 were used to study the analogous interfacial reaction, where electron transfer was the only mechanistic step. Analysis of this data with a recently reported multichannel kinetic model was used to construct a PCET zone diagram and supported the assignment of an ET-PT mechanism at pH = 5-10. Ultimately, this study represents a unique example among M ox -OH/M red -OH 2 reactivity where the protonation and oxidation states of the intermediate were kinetically and spectrally resolved to firmly establish the PCET mechanism.

The oxidation of tryptophan (Trp) is an important step in many biological processes and often occurs by sequential or concerted proton-coupled electron transfer (PCET). The apparent rate constants for the photochemical oxidation of two Trp derivatives in water have been shown to be pH-independent at low pH and to exhibit weak pH dependence at higher pH. Herein, these systems are investigated with a general, multi-channel model that includes sequential and concerted mechanisms as well as various proton donors and acceptors. This model can reproduce the kinetic data for both Trp derivatives with physically meaningful parameters and suggests that the weak pH dependence may arise from the competition between OH - and H 2 O as proton acceptors in concerted PCET. Deprotonation of an ammonium group for one of the systems leads to a more complex pH dependence at higher pH. This work demonstrates the importance of considering multiple competing channels for the analysis of the pH dependence of apparent PCET rate constants.

The coupled quantum dynamics of electrons and protons is ubiquitous in many dynamical processes involving light-matter interaction, such as solar energy conversion in chemical systems and photosynthesis. A first-principles description of such nuclear-electronic quantum dynamics requires not only the time-dependent treatment of nonequilibrium electron dynamics but also that of quantum protons. Quantum mechanical correlation between electrons and protons adds further complexity to such coupled dynamics. Here we extend real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) to periodic systems and perform first-principles simulations of coupled quantum dynamics of electrons and protons in complex heterogeneous systems. The process studied is an electronically excited-state intramolecular proton transfer of o-hydroxybenzaldehyde in water and at a silicon (111) semiconductor-molecule interface. These simulations illustrate how environments such as hydrogen-bonding water molecules and an extended material surface impact the dynamical process on the atomistic level. Depending on how the molecule is chemisorbed on the surface, excited-state electron transfer from the molecule to the semiconductor surface can inhibit ultrafast proton transfer within the molecule. This Letter elucidates how heterogeneous environments influence the balance between the quantum mechanical proton transfer and excited electron dynamics. The periodic RT-NEO-TDDFT approach is applicable to a wide range of other photoinduced heterogeneous processes.

Accurate simulations of many chemical processes require the inclusion of both nuclear quantum effects and a solvent environment. The nuclear-electronic orbital (NEO) approach, which treats electrons and select nuclei quantum mechanically on the same level, combined with a polarizable continuum model (PCM) for the solvent environment, addresses this challenge in a computationally practical manner. In this work, the NEO-PCM approach is extended beyond the IEF-PCM (integral equation formalism PCM) and C-PCM (conductor PCM) approaches to the SS(V)PE (surface and simulation of volume polarization for electrostatics) and ddCOSMO (domain decomposed conductor-like screening model) approaches. IEF-PCM, SS(V)PE, C-PCM, and ddCOSMO all exhibit similar solvation energies as well as comparable nuclear polarization within the NEO framework. The calculations show that the nuclear density does not leak out of the molecular cavity because it is much more localized than the electronic density. Finally, the polarization of quantized protons is analyzed in both continuum solvent and explicit solvent environments described by the polarizable MB-pol model, illustrating the impact of specific hydrogen-bonding interactions captured only by explicit solvation. These calculations highlight the relationship among solvation formalism, nuclear polarization, and energetics.

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.