Diabatization Schemes for Generating Charge-Localized Electron–Proton Vibronic States in Proton-Coupled Electron Transfer Systems

The interplay of covalency, cooperativity, and coupling strength in governing C-H bond activation in Ni2E2 (E = O, S, Se, Te) complexes

Dinickel dichalcogenide complexes hold vital multifaceted significance across catalysis, electron transfer, magnetism, materials science, and energy conversion. Understanding their structure, bonding, and reactivity is crucial for all aforementioned applications. These complexes are classified as dichalcogenide, subchalcogenide, or chalcogenide based on metal oxidation and coordinated chalcogen, and due to the associated complex electronic structure, ambiguity often lingers about their classification. In this work, using DFT, CASSCF/NEVPT2, and DLPNO-CCSD(T) methods, we have studied in detail [(NiL)2(E2)] (L = 1,4,7,10-tetramethyl-1,4,7,10-tetraazacyclododecane; E = O, S, Se and Te) complexes and explored their reactivity towards C-H bond activation for the first time. Through a comprehensive analysis of the structure, bonding, and reactivity of a series of [(NiL)2(E2)] complexes with E = O, S, Se, and Te, our computational findings suggest that {Ni2O2} and {Ni2S2} are best categorised as dichalcogenide-type complexes. In contrast, {Ni2Se2} and {Ni2Te2} display tendencies consistent with the subchalcogenide classification, and this aligns with the earlier structural correlation proposed (Berry and co-workers, J. Am. Chem. Soc. 2015, 137, 4993) reports on the importance of the E-E bond strength. Our study suggests the reactivity order of {Ni2O2} > {Ni2S2} > {Ni2Se2} > {Ni2Te2} for C-H bond activation, and the origin of the difference in reactivity was attributed to the difference in the Ni-E bond covalency, and electronic cooperativity between two Ni centres that switch among the classification during the reaction. Further non-adiabatic analysis at the C-H bond activation step demonstrates a decrease in coupling strength as we progress down the group, indicating a correlation with metal-ligand covalency. Notably, the reactivity trend is found to be correlated to the strength of the antiferromagnetic exchange coupling constant J via developing a magneto-structural-barrier map - offering a hitherto unknown route to fine-tune the reactivity of this important class of compound.

A fast and smooth one-electron approach for investigating charge transfer states and D1-D0 crossings for systems with odd numbers of electrons

We propose an efficient version of ensemble Hartree-Fock/density functional theory to calculate a set of two charge-transfer states for systems with odd-numbers of electrons. The approach does require definitions of donor/acceptor fragments; however, the approach is not very sensitive to such definitions-even in the limit of very strong electronic coupling. The key ansatz is that, by mandating that the vector space spanned by the active orbitals projects equally onto the donor and acceptor fragments, such a constraint eliminates all intra-molecular local excitations and makes it far easier to generate potential energy surfaces that are smooth over a wide region of configuration space. The method is fast, working with only two electron configurations, and should be useful for ab initio non-adiabatic dynamics in the near future.

Radical ligand transfer: mechanism and reactivity governed by three-component thermodynamics

Here, we demonstrate that the relationship between reactivity and thermodynamics in radical ligand transfer chemistry can be understood if this chemistry is dissected as concerted ion-electron transfer (cIET). Namely, we investigate radical ligand transfer reactions from the perspective of thermodynamic contributions to the reaction barrier: the diagonal effect of the free energy of the reaction, and the off-diagonal effect resulting from asynchronicity and frustration, which we originally derived from the thermodynamic cycle for concerted proton-electron transfer (cPET). This study on the OH transfer reaction shows that the three-component thermodynamic model goes beyond cPET chemistry, successfully capturing the changes in radical ligand transfer reactivity in a series of model FeIII-OH⋯(diflouro)cyclohexadienyl systems. We also reveal the decisive role of the off-diagonal thermodynamics in determining the reaction mechanism. Two possible OH transfer mechanisms, in which electron transfer is coupled with either OH- and OH+ transfer, are associated with two competing thermodynamic cycles. Consequently, the operative mechanism is dictated by the cycle yielding a more favorable off-diagonal effect on the barrier. In line with this thermodynamic link to the mechanism, the transferred OH group in OH-/electron transfer retains its anionic character and slightly changes its volume in going from the reactant to the transition state. In contrast, OH+/electron transfer develops an electron deficiency on OH, which is evidenced by an increase in charge and a simultaneous decrease in volume. In addition, the observations in the study suggest that an OH+/electron transfer reaction can be classified as an adiabatic radical transfer, and the OH-/electron transfer reaction as a less adiabatic ion-coupled electron transfer.

Geometrical decomposition of nonadiabatic interactions to collective coordinates in many-dimensional and many-state mixed fast-slow dynamics

In general, for many-dimensional and many-state nonadiabatic dynamics composed of slow and fast modes, we geometrically decompose the nonadiabatic interactions by means of the method of singular value decomposition. Each pair of the left and right singular vectors connecting the slow (nuclear) and fast (electronic) modes gives rise to a one-dimensional collective coordinate, and the sum of them amounts to the total nonadiabatic interaction. The analysis identifies how efficiently the slow modes, thus decomposed, can induce a transition in their fast counterparts. We discuss the notions of nonadiabatic resonance and nonadiabatic chaos in terms of the decomposition.

The Marcus dimension: identifying the nuclear coordinate for electron transfer from ab initio calculations

The Marcus model forms the foundation for all modern discussion of electron transfer (ET). In this model, ET results in a change in diabatic potential energy surfaces, separated along an ET nuclear coordinate. This coordinate accounts for all nuclear motion that promotes electron transfer. It is usually assumed to be dominated by a collective asymmetric vibrational motion of the redox sites involved in the ET. However, this coordinate is rarely quantitatively specified. Instead, it remains a nebulous concept, rather than a tool for gaining true insight into the ET pathway. Herein, we describe an ab initio approach for quantifying the ET coordinate and demonstrate it for a series of dinitroradical anions. Using sampling methods at finite temperature combined with density functional theory calculations, we find that the electron transfer can be followed using the energy separation between potential energy surfaces and the extent of electron localization. The precise nuclear motion that leads to electron transfer is then obtained as a linear combination of normal modes. Once the coordinate is identified, we find that evolution along it results in a change in diabatic state and optical excitation energy, as predicted by the Marcus model. Thus, we conclude that a single dimension of the electron transfer described in Marcus-Hush theory can be described as a well-defined nuclear motion. Importantly, our approach allows the separation of the intrinsic electron transfer coordinate from other structural relaxations and environmental influences. Furthermore, the barrier separating the adiabatic minima was found to be sufficiently thin to enable heavy-atom tunneling in the ET process.

Theoretical study on hydrogen transfer in the dissociation of dimethyl disulfide radical cations

Hydrogen transfer (HT) is of crucial importance in biochemistry and atmospheric chemistry. Here, HT processes involved in the dissociation reaction of dimethyl disulfide radical cations (DMDS˙⁺, CH₃SSCH₃˙⁺) are investigated using quantum chemical calculations. Four HTs from the C to S atom and one HT from the S to S atom are observed and the most probable paths are proposed in the dissociation channel from DMDS˙⁺ to CH_nS⁺ (n = 2-4). The mechanisms of all these five HTs are described as hydrogen atom transfer (HAT) and four of them are accompanied by electron transfer (ET). Considering the catalytic effect of water molecules existing in organisms and the atmosphere, five HT processes in the dissociation of the [DMDS + H₂O]˙⁺ complex are further explored, which show lower free energy barriers. With the participation of water molecules acting as a base, two HTs from the C to the S atom, which have the largest decrease in energy barriers, are characterized as concerted proton-coupled electron transfer (cPCET). These results can be extended to understand the mechanism of the HT process during the dissociation of disulfide and help provide a strategy to design a rare cPCET mechanism for the activation of the C-H bond.

Theoretical Modeling of Electrochemical Proton-Coupled Electron Transfer

Proton-coupled electron transfer (PCET) plays an essential role in a wide range of electrocatalytic processes. A vast array of theoretical and computational methods have been developed to study electrochemical PCET. These methods can be used to calculate redox potentials and pK_a values for molecular electrocatalysts, proton-coupled redox potentials and bond dissociation free energies for PCET at metal and semiconductor interfaces, and reorganization energies associated with electrochemical PCET. Periodic density functional theory can also be used to compute PCET activation energies and perform molecular dynamics simulations of electrochemical interfaces. Various approaches for maintaining a constant electrode potential in electronic structure calculations and modeling complex interactions in the electric double layer (EDL) have been developed. Theoretical formulations for both homogeneous and heterogeneous electrochemical PCET spanning the adiabatic, nonadiabatic, and solvent-controlled regimes have been developed and provide analytical expressions for the rate constants and current densities as functions of applied potential. The quantum mechanical treatment of the proton and inclusion of excited vibronic states have been shown to be critical for describing experimental data, such as Tafel slopes and potential-dependent kinetic isotope effects. The calculated rate constants can be used as input to microkinetic models and voltammogram simulations to elucidate complex electrocatalytic processes.

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

Path Integrals for Nonadiabatic Dynamics: Multistate Ring Polymer Molecular Dynamics

This review focuses on a recent class of path-integral-based methods that simulate nonadiabatic dynamics in the condensed phase using only classical molecular dynamics trajectories in an extended phase space. Specifically, a semiclassical mapping protocol is used to derive an exact, continuous, Cartesian variable path-integral representation for the canonical partition function of a system in which multiple electronic states are coupled to nuclear degrees of freedom. Building on this exact statistical foundation, multistate ring polymer molecular dynamics methods are developed for the approximate calculation of real-time thermal correlation functions. The remarkable promise of these multistate ring polymer methods, their successful applications, and their limitations are discussed in detail.Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Ab initio symmetric quasi-classical approach to investigate molecular Tully models

We perform on-the-fly non-adiabatic molecular dynamics simulations using the symmetrical quasi-classical (SQC) approach with the recently suggested molecular Tully models: ethylene and fulvene. We attempt to provide benchmarks of the SQC methods using both the square and triangle windowing schemes as well as the recently proposed electronic zero-point-energy correction scheme (the so-called γ correction). We use the quasi-diabatic propagation scheme to directly interface the diabatic SQC methods with adiabatic electronic structure calculations. Our results showcase the drastic improvement of the accuracy by using the trajectory-adjusted γ-corrections, which outperform the widely used trajectory surface hopping method with decoherence corrections. These calculations provide useful and non-trivial tests to systematically investigate the numerical performance of various diabatic quantum dynamics approaches, going beyond simple diabatic model systems that have been used as the major workhorse in the quantum dynamics field. At the same time, these available benchmark studies will also likely foster the development of new quantum dynamics approaches based on these techniques.

Theoretical Description of the Primary Proton-Coupled Electron Transfer Reaction in the Cytochrome bc1 Complex

The cytochrome bc₁ complex is a transmembrane enzymatic protein complex that plays a central role in cellular energy production and is present in both photosynthetic and respiratory chain organelles. Its reaction mechanism is initiated by the binding of a quinol molecule to an active site, followed by a series of charge transfer reactions between the quinol and protein subunits. Previous work hypothesized that the primary reaction was a concerted proton-coupled electron transfer (PCET) reaction because of the apparent absence of intermediate states associated with single proton or electron transfer reactions. In the present study, the kinetics of the primary bc₁ complex PCET reaction is investigated with a vibronically nonadiabatic PCET theory in conjunction with all-atom molecular dynamics simulations and electronic structure calculations. The computed rate constants and relatively high kinetic isotope effects are consistent with experimental measurements on related biomimetic systems. The analysis implicates a concerted PCET mechanism with significant hydrogen tunneling and nonadiabatic effects in the bc₁ complex. Moreover, the employed theoretical framework is shown to serve as a general strategy for describing PCET reactions in bioenergetic systems.

Nuclear-Electronic Orbital Multistate Density Functional Theory

Hydrogen tunneling is essential for a wide range of chemical and biological processes. The description of hydrogen tunneling with multicomponent quantum chemistry approaches, where the transferring hydrogen nucleus is treated on the same level as the electrons, is challenging due to the importance of both static and dynamical electron-proton correlation. Herein the nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method is presented as a strategy to include both types of correlation. In this approach, two localized nuclear-electronic wave functions obtained with the NEO-DFT method are combined with a nonorthogonal configurational interaction approach to produce bilobal, delocalized ground and excited vibronic states. By including a correction function, the NEO-MSDFT approach can produce quantitatively accurate hydrogen tunneling splittings for fixed geometries of systems such as malonaldehyde and acetoacetaldehyde. This approach is computationally efficient and can be combined with methods such as vibronic coupling theory to describe tunneling dynamics and to compute vibronic couplings in many types of systems.

Exploring the write-in process in molecular quantum cellular automata: a combined modelingand first-principle approach

The molecular quantum cellular automata paradigm (m-QCA) offers a promising alternative framework to current CMOS implementations. A crucial aspect for implementing this technology concerns the construction of a device which effectively controls intramolecular charge-transfer processes. Tentative experimental implementations have been developed in which a voltage drop is created generating the forces that drive a molecule into a logic state. However, important factors such as the electric field profile, its possible time-dependency and the influence of temperature in the overall success of charge-transfer are relevant issues to be considered in the design of a reliable device. In this work, we theoretically study the role played by these processes in the overall intramolecular charge-transfer process. We have used a Landau-Zener (LZ) model, where different time-dependent electric field profiles have been simulated. The results have been further corroborated employing density functional tight-binding method. The role played by the nuclear motions in the electron-transfer process has been investigated beyond the Born-Oppenheimer approximation by computing the effect of the external electric field in the behavior of the potential energy surface. Hence, we demonstrate that the intramolecular charge-transfer process is a direct consequence of the coherent LZ nonadiabatic tunneling and the hybridization of the diabatic vibronic states which effectively reduces the trapping of the itinerant electron at the donor group.

Kinetics of Proton Discharge on Metal Electrodes: Effects of Vibrational Nonadiabaticity and Solvent Dynamics

Proton discharge on metal electrodes, also denoted the Volmer reaction, is a critical step in a wide range of electrochemical processes. This electrochemical proton-coupled electron transfer (PCET) reaction is predominantly electronically adiabatic in aqueous solution and is typically treated as fully adiabatic. Recently, a theoretical model for this PCET reaction was developed to generate the vibronic free energy surfaces as functions of a collective solvent coordinate and the distance of the proton-donating acid from the electrode. Herein a unified formulation is devised to describe such PCET reactions in terms of a curve crossing between two diabatic vibronic states corresponding to the lowest two proton vibrational states, employing an interpolation scheme that spans the adiabatic transition state theory, nonadiabatic Fermi golden rule, and solvent-controlled regimes. In contrast to previous treatments, application of this formulation to the aqueous Volmer reaction highlights the importance of vibrational nonadiabaticity and solvent dynamics. The calculated transfer coefficients and kinetic isotope effects are in reasonable agreement with experimental measurements. These fundamental insights have broad implications for understanding electrochemical processes.

Diabatic model for electrochemical hydrogen evolution based on constrained DFT configuration interaction

The accuracy of density functional theory (DFT) based kinetic models for electrocatalysis is diminished by spurious electron delocalization effects, which manifest as uncertainties in the predicted values of reaction and activation energies. In this work, we present a constrained DFT (CDFT) approach to alleviate overdelocalization effects in the Volmer-Heyrovsky mechanism of the hydrogen evolution reaction (HER). This method is applied a posteriori to configurations sampled along a reaction path to correct their relative stabilities. Concretely, the first step of this approach involves describing the reaction in terms of a set of diabatic states that are constructed by imposing suitable density constraints on the system. Refined reaction energy profiles are then recovered by performing a configuration interaction (CDFT-CI) calculation within the basis spanned by the diabatic states. After a careful validation of the proposed method, we examined HER catalysis on open-ended carbon nanotubes and discovered that CDFT-CI increased activation energies and decreased reaction energies relative to DFT predictions. We believe that a similar approach could also be adopted to treat overdelocalization effects in other electrocatalytic proton-coupled electron transfer reactions, e.g., in the oxygen reduction reaction.

Proton-coupled electron transfer reactions: analytical rate constants and case study of kinetic isotope effects in lipoxygenase

A general theory has been developed for proton-coupled electron transfer (PCET), which is vital to a wide range of chemical and biological processes. This theory describes PCET reactions in terms of nonadiabatic transitions between reactant and product electron-proton vibronic states and includes the effects of thermal fluctuations of the solvent or protein environment, as well as the proton donor-acceptor motion. Within the framework of this general PCET theory, a series of analytical rate constant expressions has been derived for PCET reactions in well-defined regimes. Herein, the application of this theory to PCET in the enzyme soybean lipoxygenase illustrates the regimes of validity for the various rate constant expressions and elucidates the fundamental physical principles dictating PCET reactions. Such theoretical studies provide significant physical insights that guide the interpretation of experimental data and lead to experimentally testable predictions. A combination of theoretical treatments with atomic-level simulations is essential to understanding PCET.

cPCET versus HAT: A Direct Theoretical Method for Distinguishing X-H Bond-Activation Mechanisms

Proton‐coupled electron transfer (PCET) events play a key role in countless chemical transformations, but they come in many physical variants which are hard to distinguish experimentally. While present theoretical approaches to treat these events are mostly based on physical rate coefficient models of various complexity, it is now argued that it is both feasible and fruitful to directly analyze the electronic N‐electron wavefunctions of these processes along their intrinsic reaction coordinate (IRC). In particular, for model systems of lipoxygenase and the high‐valent oxoiron(IV) intermediate TauD‐J it is shown that by invoking the intrinsic bond orbital (IBO) representation of the wavefunction, the common boundary cases of hydrogen atom transfer (HAT) and concerted PCET (cPCET) can be directly and unambiguously distinguished in a straightforward manner.

Diabatization for Time-Dependent Density Functional Theory: Exciton Transfers and Related Conical Intersections

Intermolecular exciton transfers and related conical intersections are analyzed by diabatization for time-dependent density functional theory. The diabatic states are expressed as a linear combination of the adiabatic states so as to emulate the well-defined reference states. The singlet exciton coupling calculated by the diabatization scheme includes contributions from the Coulomb (Förster) and electron exchange (Dexter) couplings. For triplet exciton transfers, the Dexter coupling, charge transfer integral, and diabatic potentials of stacked molecules are calculated for analyzing direct and superexchange pathways. We discuss some topologies of molecular aggregates that induce conical intersections on the vanishing points of the exciton coupling, namely boundary of H- and J-aggregates and T-shape aggregates, as well as canceled exciton coupling to the bright state of H-aggregate, i.e., selective exciton transfer to the dark state. The diabatization scheme automatically accounts for the Berry phase by fixing the signs of reference states while scanning the coordinates.

Dependence of Vibronic Coupling on Molecular Geometry and Environment: Bridging Hydrogen Atom Transfer and Electron-Proton Transfer

The rate constants for typical concerted proton-coupled electron transfer (PCET) reactions depend on the vibronic coupling between the diabatic reactant and product states. The form of the vibronic coupling is different for electronically adiabatic and nonadiabatic reactions, which are associated with hydrogen atom transfer (HAT) and electron-proton transfer (EPT) mechanisms, respectively. Most PCET rate constant expressions rely on the Condon approximation, which assumes that the vibronic coupling is independent of the nuclear coordinates of the solute and the solvent or protein. Herein we test the Condon approximation for PCET vibronic couplings. The dependence of the vibronic coupling on molecular geometry is investigated for an open and a stacked transition state geometry of the phenoxyl-phenol self-exchange reaction. The calculations indicate that the open geometry is electronically nonadiabatic, corresponding to an EPT mechanism that involves significant electronic charge redistribution, while the stacked geometry is predominantly electronically adiabatic, corresponding primarily to an HAT mechanism. Consequently, a single molecular system can exhibit both HAT and EPT character. The dependence of the vibronic coupling on the solvent or protein configuration is examined for the soybean lipoxygenase enzyme. The calculations indicate that this PCET reaction is electronically nonadiabatic with a vibronic coupling that does not depend significantly on the protein environment. Thus, the Condon approximation is shown to be valid for the solvent and protein nuclear coordinates but invalid for the solute nuclear coordinates in certain PCET systems. These results have significant implications for the calculation of rate constants, as well as mechanistic interpretations, of PCET reactions.

The requisite electronic structure theory to describe photoexcited nonadiabatic dynamics: nonadiabatic derivative couplings and diabatic electronic couplings

Electronically photoexcited dynamics are complicated because there are so many different relaxation pathways: fluorescence, phosphorescence, radiationless decay, electon transfer, etc. In practice, to model photoexcited systems is a very difficult enterprise, requiring accurate and very efficient tools in both electronic structure theory and nonadiabatic chemical dynamics. Moreover, these theoretical tools are not traditional tools. On the one hand, the electronic structure tools involve couplings between electonic states (rather than typical single state energies and gradients). On the other hand, the dynamics tools involve propagating nuclei on multiple potential energy surfaces (rather than the usual ground state dynamics). In this Account, we review recent developments in electronic structure theory as directly applicable for modeling photoexcited systems. In particular, we focus on how one may evaluate the couplings between two different electronic states. These couplings come in two flavors. If we order states energetically, the resulting adiabatic states are coupled via derivative couplings. Derivative couplings capture how electronic wave functions change as a function of nuclear geometry and can usually be calculated with straightforward tools from analytic gradient theory. One nuance arises, however, in the context of time-dependent density functional theory (TD-DFT): how do we evaluate derivative couplings between TD-DFT excited states (which are tricky, because no wave function is available)? This conundrum was recently solved, and we review the solution below. We also discuss the solution to a second, pesky problem of origin dependence, whereby the derivative couplings do not (strictly) satisfy translation variance, which can lead to a lack of momentum conservation. Apart from adiabatic states, if we order states according to their electronic character, the resulting diabatic states are coupled via electronic or diabatic couplings. The couplings between diabatic states |ΞA⟩ and |ΞB⟩ are just the simple matrix elements, ⟨ΞA|H|ΞB⟩. A difficulty arises, however, because constructing exactly diabatic states is formally impossible and constructing quasi-diabatic states is not unique. To that end, we review recent advances in localized diabatization, which is one approach for generating adiabatic-to-diabatic (ATD) transformations. We also highlight outstanding questions in the arena of diabatization, especially how to generate multiple globally stable diabatic surfaces.

Block diagonalization of the equation-of-motion coupled cluster effective Hamiltonian: treatment of diabatic potential constants and triple excitations

We present a diabatization method applicable to spectroscopic studies based on Equation-of-Motion Coupled Cluster (EOM-CC) energies and biorthogonal wavefunctions that uses the Block Diagonalization (BD) approaches of Cederbaum et al. [L. S. Cederbaum, J. Schirmer, and H. D. Meyer, J. Phys. A: Math. Gen. 22, 2427 (1989)] and Domcke et al. [W. Domcke and C. Woywod, Chem. Phys. Lett. 216, 362 (1993); W. Domcke, C. Woywod, and M. Stengle, Chem. Phys. Lett. 226, 257 (1994)]. The method gives excellent agreement with coupling constants calculated using the analytic gradient approach of Ichino et al. [T. Ichino, J. Gauss, and J. F. Stanton, J. Chem. Phys. 130, 174105 (2009)]. While the BD method is a finite difference approach, it can be applied at any geometry, can generate (pointwise) diabatic potential energy surfaces, and can be used with EOM wavefunctions that include triple (or higher) excitations. The method is applied to several model systems and its sensitivity to orbital choice, excitation space, and projection space is explored.

A unified diabatic description for electron transfer reactions, isomerization reactions, proton transfer reactions, and aromaticity

A way is found for describing general chemical reactions using diabatic multi-state and “twin-state” models. (Image adapted with permission from https://www.flickr.com/photos/cybaea/64638988/).

Bond angle variations in XH3 [X = N, P, As, Sb, Bi]: the critical role of Rydberg orbitals exposed using a diabatic state model

The origins of the observed bond angles in XH₃ and XH₃⁺ are explained using high-level calculations and a simple diabatic model.

Analysis of geometric phase effects in the quantum-classical Liouville formalism

We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.

Probing Nonadiabaticity in the Proton-Coupled Electron Transfer Reaction Catalyzed by Soybean Lipoxygenase

Proton-coupled electron transfer (PCET) plays a vital role in many biological and chemical processes. PCET rate constant expressions are available for various well-defined regimes, and determining which expression is appropriate for a given system is essential for reliable modeling. Quantitative diagnostics have been devised to characterize the vibronic nonadiabaticity between the electron-proton quantum subsystem and the classical nuclei, as well as the electron-proton nonadiabaticity between the electrons and proton(s) within the quantum subsystem. Herein these diagnostics are applied to a model of the active site of the enzyme soybean lipoxygenase, which catalyzes a PCET reaction that exhibits unusually high deuterium kinetic isotope effects at room temperature. Both semiclassical and electronic charge density diagnostics illustrate vibronic and electron-proton nonadiabaticity for this PCET reaction, supporting the use of the Golden rule nonadiabatic rate constant expression with a specific form of the vibronic coupling. This type of characterization will be useful for theoretical modeling of a broad range of PCET processes.

Intermolecular proton shuttling in excited state proton transfer reactions: insights from theory

The mechanism of intermolecular proton shuttling involved in a prototypical excited state proton transfer reaction is disclosed using DFT and TD-DFT.

Multistate treatments of the electronic coupling in donor-bridge-acceptor systems: insights and caveats from a simple model

We use a simple one-dimensional delta function electronic structure model (dfm) to investigate the results of a pair of multistate diabatization techniques (i.e., based on n states, with n ≥ 2) for linear DBA and DBBA (donor-bridge-acceptor) electron-transfer systems. In particular, we focus on the physical meaning of the couplings obtained from multistate methods and their relationship to two-state (n = 2) coupling elements. On the basis of the simple dfm approach, which allows exact as well as finite basis set treatment and has no many-electron effects, we conclude that for orthogonal diabatic states, it is difficult to assign clear physical significance to multistate matrix elements for coupling beyond nearest-neighbor contacts. The implications of these results for more complex multistate many-electron treatments are discussed. It is emphasized that physically meaningful coupling elements must involve states that are orthogonal, either explicitly or implicitly.

Excited-state proton coupled charge transfer modulated by molecular structure and media polarization

Charge and proton transfer reactions in the excited states of organic dyes can be coupled in many different ways. Despite the complementarity of charges, they can occur on different time scales and in different directions of the molecular framework. In certain cases, excited-state equilibrium can be established between the charge-transfer and proton-transfer species. The interplay of these reactions can be modulated and even reversed by variations in dye molecular structures and changes of the surrounding media. With knowledge of the mechanisms of these processes, desired rates and directions can be achieved, and thus the multiple emission spectral features can be harnessed. These features have found versatile applications in a number of cutting-edge technological areas, particularly in fluorescence sensing and imaging.