The Third Dimension of a More O'Ferrall-Jencks Diagram for Hydrogen Atom Transfer in the Isoelectronic Hydrogen Exchange Reactions of (PhX)(2)H(•) with X = O, NH, and CH(2)

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.

Mechanisms and energetics for hydrogen abstraction of thymine photosensitized by benzophenone from theoretical principles

The significant role of hydrogen abstraction in chemistry and biology has inspired many theoretical works to link its practical phenomena and mechanistic properties. Here, the photophysical processes and hydrogen abstraction mechanisms of benzophenone (BZP) photosensitized thymine damage were systematically investigated from theoretical principles. It was found that the BZP photosensitizer upon UV irradiation undergoes vertical excitation, internal conversion, vibrational relaxation and intersystem crossing into a triplet excited state. Then the triplet BZP damages thymine by a hydrogen abstraction process. However, the reverse reaction easily occurs due to the lower reaction energy, which causes a low yield of hydrogen abstraction products. We hope this comprehensive work can provide a deeper understanding of photosensitive DNA damage from hydrogen abstraction.

Subsystem density-functional theory: A reliable tool for spin-density based properties

Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.

Minimal Active Space for Diradicals Using Multistate Density Functional Theory

This work explores the electronic structure as well as the reactivity of singlet diradicals, making use of multistate density functional theory (MSDFT). In particular, we show that a minimal active space of two electrons in two orbitals is adequate to treat the relative energies of the singlet and triplet adiabatic ground state as well as the first singlet excited state in many cases. This is plausible because dynamic correlation is included in the first place in the optimization of orbitals in each determinant state via block-localized Kohn–Sham density functional theory. In addition, molecular fragment, i.e., block-localized Kohn–Sham orbitals, are optimized separately for each determinant, providing a variational diabatic representation of valence bond-like states, which are subsequently used in nonorthogonal state interactions (NOSIs). The computational procedure and its performance are illustrated on some prototypical diradical species. It is shown that NOSI calculations in MSDFT can be used to model bond dissociation and hydrogen-atom transfer reactions, employing a minimal number of configuration state functions as the basis states. For p- and s-types of diradicals, the closed-shell diradicals are found to be more reactive than the open-shell ones due to a larger diabatic coupling with the final product state. Such a diabatic representation may be useful to define reaction coordinates for electron transfer, proton transfer and coupled electron and proton transfer reactions in condensed-phase simulations.

Minimal-active-space multistate density functional theory for excitation energy involving local and charge transfer states

Multistate density functional theory (MSDFT) employing a minimum active space (MAS) is presented to determine charge transfer (CT) and local excited states of bimolecular complexes. MSDFT is a hybrid wave function theory (WFT) and density functional theory, in which dynamic correlation is first incorporated in individual determinant configurations using a Kohn-Sham exchange-correlation functional. Then, nonorthogonal configuration-state interaction is performed to treat static correlation. Because molecular orbitals are optimized separately for each determinant by including Kohn-Sham dynamic correlation, a minimal number of configurations in the active space, essential to representing low-lying excited and CT states of interest, is sufficient to yield the adiabatic states. We found that the present MAS-MSDFT method provides a good description of covalent and CT excited states in comparison with experiments and high-level computational results. Because of the simplicity and interpretive capability through diabatic configuration weights, the method may be useful in dynamic simulations of CT and nonadiabatic processes.

Exact-two-component block-localized wave function: A simple scheme for the automatic computation of relativistic ΔSCF

Block-localized wave function is a useful method for optimizing constrained determinants. In this article, we extend the generalized block-localized wave function technique to a relativistic two-component framework. Optimization of excited state determinants for two-component wave functions presents a unique challenge because the excited state manifold is often quite dense with degenerate states. Furthermore, we test the degree to which certain symmetries result naturally from the ΔSCF optimization such as time-reversal symmetry and symmetry with respect to the total angular momentum operator on a series of atomic systems. Variational optimizations may often break the symmetry in order to lower the overall energy, just as unrestricted Hartree-Fock breaks spin symmetry. Overall, we demonstrate that time-reversal symmetry is roughly maintained when using Hartree-Fock, but less so when using Kohn-Sham density functional theory. Additionally, maintaining total angular momentum symmetry appears to be system dependent and not guaranteed. Finally, we were able to trace the breaking of total angular momentum symmetry to the relaxation of core electrons.

Statistical analysis of C-H activation by oxo complexes supports diverse thermodynamic control over reactivity

Transition metal oxo species are key intermediates for the activation of strong C-H bonds. As such, there has been interest in understanding which structural or electronic parameters of metal oxo complexes determine their reactivity. Factors such as ground state thermodynamics, spin state, steric environment, oxygen radical character, and asynchronicity have all been cited as key contributors, yet there is no consensus on when each of these parameters is significant or the relative magnitude of their effects. Herein, we present a thorough statistical analysis of parameters that have been proposed to influence transition metal oxo mediated C-H activation. We used density functional theory (DFT) to compute parameters for transition metal oxo complexes and analyzed their ability to explain and predict an extensive data set of experimentally determined reaction barriers. We found that, in general, only thermodynamic parameters play a statistically significant role. Notably, however, there are independent and significant contributions from the oxidation potential and basicity of the oxo complexes which suggest a more complicated thermodynamic picture than what has been shown previously.

Block-Localized Excitation for Excimer Complex and Diabatic Coupling

We describe a block-localized excitation (BLE) method to carry out constrained optimization of block-localized orbitals for constructing valence bond-like, diabatic excited configurations using multistate density functional theory (MSDFT). The method is an extension of the previous block-localized wave function method through a fragment-based ΔSCF approach to optimize excited determinants within a molecular complex. In BLE, both the number of electrons and the electronic spin of different fragments in a whole system can be constrained, whereas electrostatic, exchange, and polarization interactions among different blocks can be fully taken into account of. To avoid optimization collapse to unwanted states, a ΔSCF projection scheme and a maximum overlap of wave function approach have been presented. The method is illustrated by the excimer complex of two naphthalene molecules. With a minimum of eight spin-adapted configurational state functions, it was found that the inversion of L_a^- and L_b^- states near the optimal structure of the excimer complex is correctly produced, which is in quantitative agreement with DMRG-CASPT2 calculations and experiments. Trends in the computed transfer integrals associated with excited-state energy transfer both in the singlet and triplet states are discussed. The results suggest that MSDFT may be used as an efficient approach to treat intermolecular interactions in excited states with a minimal active space (MAS) for interpretation of the results and for dynamic simulations, although the selection of a small active space is often system dependent.

Coupled electron and proton transfer in the piperidine drug metabolism pathway by the active species of cytochromes P450

KS-DFT and MSDFT studies reveal a novel CEPT step that triggers ring contraction of piperidines by P450.

Catalytic hydrogen atom transfer from hydrosilanes to vinylarenes for hydrosilylation and polymerization

Because of the importance of hydrogen atom transfer (HAT) in biology and chemistry, there is increased interest in new strategies to perform HAT in a sustainable manner. Here, we describe a sustainable, net redox-neutral HAT process involving hydrosilanes and alkali metal Lewis base catalysts - eliminating the use of transition metal catalysts - and report an associated mechanism concerning Lewis base-catalysed, complexation-induced HAT (LBCI-HAT). The catalytic LBCI-HAT is capable of accessing both branch-specific hydrosilylation and polymerization of vinylarenes in a highly selective fashion, depending on the Lewis base catalyst used. In this process, earth abundant, alkali metal Lewis base catalyst plays a dual role. It first serves as a HAT initiator and subsequently functions as a silyl radical stabilizing group, which is critical to highly selective cross-radical coupling. EPR study identified a potassiated paramagnetic species and multistate density function theory revealed a high HAT character, yet multiconfigurational nature in the transition state of the reaction.

Theoretical study of proton coupled electron transfer reaction in the light state of the AppA BLUF photoreceptor

The BLUF (blue light sensor using flavin adenine dinucleotide) domain is widely studied as a prototype for proton coupled electron transfer (PCET) reactions in biological systems. In this work, the photo-induced concerted PCET reaction from the light state of the AppA BLUF domain is investigated. To model the simultaneous transfer of two protons in the reaction, two-dimensional potential energy surfaces for the double proton transfer are first calculated for the locally excited and charge transfer states, which are then used to obtain the vibrational wave function overlaps and the vibrational energy levels. Contributions to the PCET rate constant from each pair of vibronic states are then analyzed using the theory based on the Fermi's golden rule. We show that, the recently proposed light state structure of the BLUF domain with a tautomerized Gln63 residue is consistent with the concerted transfer of one electron and two protons. It is also found that, thermal fluctuations of the protein structure, especially the proton donor-acceptor distances, play an important role in determining the PCET reaction rate. © 2018 Wiley Periodicals, Inc.

Combined Multistate and Kohn-Sham Density Functional Theory Studies of the Elusive Mechanism of N-Dealkylation of N,N-Dimethylanilines Mediated by the Biomimetic Nonheme Oxidant FeIV(O)(N4Py)(ClO4)2

The oxidative C-H bond activation mediated by heme and nonheme enzymes and related biomimetics is one of the most interesting processes in bioinorganic and oxidative chemistry. However, the mechanisms of these reactions are still elusive and controversy due to the involvement of highly reactive metal-oxo intermediates with multiple spin states, despite extensive experimental efforts, especially for the N-dealkylation of N,N-dialkyalinines. In this work, we employed multistate density functional theory (MSDFT) and the Kohn-Sham DFT to investigate the mechanism of N-demethylation of N,N-dimethyalinines oxidized by the reaction intermediate Fe^IV(O)(N4Py)(ClO₄)₂. The Kohn-Sham DFT study demonstrated that the reaction proceeds via a rate-limiting hydrogen atom transfer (HAT) step and a subsequent barrier-free oxygen rebound step to form the carbinol product. The MSDFT investigation on the first C-H activation further showed that this step is an initial hydrogen atom abstraction that is highly correlated between CEPT and HAT, i.e., both CEPT and HAT processes make significant contributions to the mechanism before reaching the diabatic crossing point, then the valence bond character of the adiabatic ground state is switched to the CEPT product configuration. The findings from this work may be applicable to other hydrogen abstraction process.

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory

We describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation.

Constructing an Interpolated Potential Energy Surface of a Large Molecule: A Case Study with Bacteriochlorophyll a Model in the Fenna-Matthews-Olson Complex

Constructing a reliable potential energy surface (PES) is a key step toward computationally studying the chemical dynamics of any molecular system. The interpolation scheme is a useful tool that can closely follow the accuracy of quantum chemical means at a dramatically reduced computational cost. However, applying interpolation to building a PES of a large molecule is not a straightforward black-box approach, as it frequently encounters practical difficulties associated with its large dimensionality. Here, we present detailed courses of applying interpolation toward building a PES of a large chromophore molecule. We take the example of S₀ and S₁ electronic states of bacteriochlorophyll a (BChla) molecules in the Fenna-Matthews-Olson light harvesting complex. With a reduced model molecule that bears BChla's main π-conjugated ring, various practical approaches are designed for improving the PES quality in a stable manner and for fine-tuning the final surface such that the surface can be adopted for long time molecular dynamics simulations. Combined with parallel implementation, we show that interpolated mechanics/molecular mechanics (IM/MM) simulations of the entire complex in the nanosecond time scale can be conducted readily without any practical issues. With 1500 interpolation data points for each chromophore unit, the PES error relative to the reference quantum chemical calculation is found to be ∼0.15 eV in the thermally accessible region of the conformational space, together with ∼0.01 eV error in S₀ - S₁ transition energies. The performance issue related to the use of a large interpolation database within the framework of our parallel routines is also discussed.

Multistate Density Functional Theory for Effective Diabatic Electronic Coupling

Multistate density functional theory (MSDFT) is presented to estimate the effective transfer integral associated with electron and hole transfer reactions. In this approach, the charge-localized diabatic states are defined by block localization of Kohn-Sham orbitals, which constrain the electron density for each diabatic state in orbital space. This differs from the procedure used in constrained density functional theory that partitions the density within specific spatial regions. For a series of model systems, the computed transfer integrals are consistent with experimental data and show the expected exponential attenuation with the donor-acceptor separation. The present method can be used to model charge transfer reactions including processes involving coupled electron and proton transfer.

Methane activation by gold-doped titanium oxide cluster anions with closed-shell electronic structures

The reactivity of closed-shell gas phase cluster anions AuTi₃O₇^- and AuTi₃O₈^- with methane under thermal collision conditions was studied by mass spectrometric experiments and quantum chemical calculations. Methane activation was observed with the formation of AuCH₃ in both cases, while the formation of formaldehyde was also identified in the reaction system of AuTi₃O₈^-. The cooperative effect of the separated Au⁺ and O^2- ions on the clusters induces the cleavage of the first C-H bond of methane. Further activation of the second C-H bond by a peroxide ion O₂^2- leads to the formation of formaldehyde. This study shows that closed-shell species on metal oxides can be reactive enough to facilitate thermal H-CH₃ bond cleavage and the subsequent conversion.

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.

Moving protons and electrons in biomimetic systems

An enormous variety of biological redox reactions are accompanied by changes in proton content at enzyme active sites, in their associated cofactors, in substrates and/or products, and between protein interfaces. Understanding this breadth of reactivity is an ongoing chemical challenge. A great many workers have developed and investigated biomimetic model complexes to build new ways of thinking about the mechanistic underpinnings of such complex biological proton-coupled electron transfer (PCET) reactions. Of particular importance are those model reactions that involve transfer of one proton (H(+)) and one electron (e(-)), which is equivalent to transfer of a hydrogen atom (H(•)). In this Current Topic, we review key concepts in PCET reactivity and describe important advances in biomimetic PCET chemistry, with a special emphasis on research that has enhanced efforts to understand biological PCET reactions.

A tutorial for understanding chemical reactivity through the valence bond approach

This is a tutorial on the usage of valence bond (VB) diagrams for understanding chemical reactivity in general, and hydrogen atom transfer (HAT) reactivity in particular. The tutorial instructs the reader how to construct the VB diagrams and how to estimate HAT barriers from raw data, starting with the simplest reaction H + H2 and going all the way to HAT in the enzyme cytochrome P450. Other reactions are treated as well, and some unifying principles are outlined. The tutorial projects the unity of reactivity treatments, following Coulson's dictum "give me insight, not numbers", albeit with its modern twist: giving numbers and insight.

Dichotomous hydrogen atom transfer vs proton-coupled electron transfer during activation of X-H bonds (X = C, N, O) by nonheme iron-oxo complexes of variable basicity

We describe herein the hydrogen-atom transfer (HAT)/proton-coupled electron-transfer (PCET) reactivity for Fe(IV)-oxo and Fe(III)-oxo complexes (1-4) that activate C-H, N-H, and O-H bonds in 9,10-dihydroanthracene (S1), dimethylformamide (S2), 1,2-diphenylhydrazine (S3), p-methoxyphenol (S4), and 1,4-cyclohexadiene (S5). In 1-3, the iron is pentacoordinated by tris[N'-tert-butylureaylato)-N-ethylene]aminato ([H3buea](3-)) or its derivatives. These complexes are basic, in the order 3 ≫ 1 > 2. Oxidant 4, [Fe(IV)N4Py(O)](2+) (N4Py: N,N-bis(2-pyridylmethyl)bis(2-pyridyl)methylamine), is the least basic oxidant. The DFT results match experimental trends and exhibit a mechanistic spectrum ranging from concerted HAT and PCET reactions to concerted-asynchronous proton transfer (PT)/electron transfer (ET) mechanisms, all the way to PT. The singly occupied orbital along the O···H···X (X = C, N, O) moiety in the TS shows clearly that in the PCET cases, the electron is transferred separately from the proton. The Bell-Evans-Polanyi principle does not account for the observed reactivity pattern, as evidenced by the scatter in the plot of calculated barrier vs reactions driving forces. However, a plot of the deformation energy in the TS vs the respective barrier provides a clear signature of the HAT/PCET dichotomy. Thus, in all C-H bond activations, the barrier derives from the deformation energy required to create the TS, whereas in N-H/O-H bond activations, the deformation energy is much larger than the corresponding barrier, indicating the presence of a stabilizing interaction between the TS fragments. A valence bond model is used to link the observed results with the basicity/acidity of the reactants.