Proton-coupled electron transfer versus hydrogen atom transfer in benzyl/toluene,methoxyl/methanol,and phenoxyl/phenol self-exchange reactions

Degenerate hydrogen atom exchange reactions have been studied using calculations, based on density functional theory (DFT), for (i) benzyl radical plus toluene, (ii) phenoxyl radical plus phenol, and (iii) methoxyl radical plus methanol. The first and third reactions occur via hydrogen atom transfer (HAT) mechanisms. The transition structure (TS) for benzyl/toluene hydrogen exchange has C(2)(h)() symmetry and corresponds to the approach of the 2p-pi orbital on the benzylic carbon of the radical to a benzylic hydrogen of toluene. In this TS, and in the similar C(2) TS for methoxyl/methanol hydrogen exchange, the SOMO has significant density in atomic orbitals that lie along the C-H vectors in the former reaction and nearly along the O-H vectors in the latter. In contrast, the SOMO at the phenoxyl/phenol TS is a pi symmetry orbital within each of the C(6)H(5)O units, involving 2p atomic orbitals on the oxygen atoms that are essentially orthogonal to the O.H.O vector. The transferring hydrogen in this reaction is a proton that is part of a typical hydrogen bond, involving a sigma lone pair on the oxygen of the phenoxyl radical and the O-H bond of phenol. Because the proton is transferred between oxygen sigma orbitals, and the electron is transferred between oxygen pi orbitals, this reaction should be described as a proton-coupled electron transfer (PCET). The PCET mechanism requires the formation of a hydrogen bond, and so is not available for benzyl/toluene exchange. The preference for phenoxyl/phenol to occur by PCET while methoxyl/methanol exchange occurs by HAT is traced to the greater pi donating ability of phenyl over methyl. This results in greater electron density on the oxygens in the PCET transition structure for phenoxyl/phenol, as compared to the PCET hilltop for methoxyl/methanol, and the greater electron density on the oxygens selectively stabilizes the phenoxyl/phenol TS by providing a larger binding energy of the transferring proton.     

Reassessment of the Mechanisms of Thermal C−H Bond Activation of Methane by Cationic Magnesium Oxides: A Critical Evaluation of the Suitability of Different Density Functionals

The mechanisms of the thermal reactions of the two iconic magnesium oxide cations MgO^.+ and Mg₂O₂^.+ with methane have been re-evaluated at the CCSD(T)/CBS//CCSD/def2-TZVP level of theory. For the reaction of MgO^.+ with CH₄, only the classical hydrogen-atom transfer (HAT) was found; in contrast, for the Mg₂O₂^.+/CH₄ couple, both HAT and proton-coupled electron-transfer (PCET) exist as mechanistic variants. In order to evaluate the suitability of density functional theory (DFT) methods, the reactions were computed by using 27 density functionals. The results obtained demonstrate that the various DFT methods often deliver rather different results for both geometric and energetic features. As to the prediction of the apparent barriers, pure functionals give the largest mean absolute errors. BMK, ωB97XD, and the double-hybrid functional mPW2PLYP were confirmed to come closest to the results provided by CCSD(T)/CBS. Thus, mechanistic conclusions based on a single DFT method should be viewed with great caution. In summary, this study may assist in the selection of a suitable quantum chemical method to unravel the mechanistic details of C−H bond activation by charged metal oxides.     

Proton-coupled electron transfer in solution, proteins, and electrochemistry

Recent advances in the theoretical treatment of proton-coupled electron transfer (PCET) reactions are reviewed. These reactions play an important role in a wide range of biological processes, as well as in fuel cells, solar cells, chemical sensors, and electrochemical devices. A unified theoretical framework has been developed to describe both sequential and concerted PCET, as well as hydrogen atom transfer (HAT). A quantitative diagnostic has been proposed to differentiate between HAT and PCET in terms of the degree of electronic nonadiabaticity, where HAT corresponds to electronically adiabatic proton transfer and PCET corresponds to electronically nonadiabatic proton transfer. In both cases, the overall reaction is typically vibronically nonadiabatic. A series of rate constant expressions have been derived in various limits by describing the PCET reactions in terms of nonadiabatic transitions between electron-proton vibronic states. These expressions account for the solvent response to both electron and proton transfer and the effects of the proton donor-acceptor vibrational motion. The solvent and protein environment can be represented by a dielectric continuum or described with explicit molecular dynamics. These theoretical treatments have been applied to numerous PCET reactions in solution and proteins. Expressions for heterogeneous rate constants and current densities for electrochemical PCET have also been derived and applied to model systems.     

Hydrogen-abstraction reactivity patterns from A to Y: the valence bond way

"Give us insight, not numbers" was Coulson's admonition to theoretical chemists. This Review shows that the valence bond (VB)-model provides insights and some good numbers for one of the fundamental reactions in nature, the hydrogen-atom transfer (HAT). The VB model is applied to over 50 reactions from the simplest H + H(2) process, to P450 hydroxylations and H-transfers among closed-shell molecules; for each system the barriers are estimated from raw data. The model creates a bridge to the Marcus equation and shows that H-atom abstraction by a closed-shell molecule requires a higher barrier owing to the additional promotion energy needed to prepare the abstractor for H-abstraction. Under certain conditions, a closed-shell abstractor can bypass this penalty through a proton-coupled electron transfer (PCET) mechanism. The VB model links the HAT and PCET mechanisms conceptually and shows the consequences that this linking has for H-abstraction reactivity.     

MPW1K Performs Much Better than B3LYP in DFT Calculations on Reactions that Proceed by Proton-Coupled Electron Transfer (PCET)

DFT calculations have been performed with the B3LYP and MPW1K functional on the hydrogen atom abstraction reactions of ethenoxyl with ethenol and of phenoxyl with both phenol and alpha-naphthol. Comparison with the results of G3 calculations shows that B3LYP seriously underestimates the barrier heights for the reaction of ethenoxyl with ethenol by both proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms. The MPW1K functional also underestimates the barrier heights, but by much less than B3LYP. Similarly, comparison with the results of experiments on the reaction of phenoxyl radical with alpha-naphthol indicates that the barrier height for the preferred PCET mechanism is calculated more accurately by MPW1K than by B3LYP. These findings indicate that the MPW1K functional is much better suited than B3LYP for calculations on hydrogen abstraction reactions by both HAT and PCET mechanisms.     

Reaction of phenols with the 2,2-diphenyl-1-picrylhydrazyl radical. Kinetics and DFT calculations applied to determine ArO-H bond dissociation enthalpies and reaction mechanism

The formal H-atom abstraction by the 2,2-diphenyl-1-picrylhydrazyl (dpph(*)) radical from 27 phenols and two unsaturated hydrocarbons has been investigated by a combination of kinetic measurements in apolar solvents and density functional theory (DFT). The computed minimum energy structure of dpph(*) shows that the access to its divalent N is strongly hindered by an ortho H atom on each of the phenyl rings and by the o-NO(2) groups of the picryl ring. Remarkably small Arrhenius pre-exponential factors for the phenols [range (1.3-19) x 10(5) M(-1) s(-1)] are attributed to steric effects. Indeed, the entropy barrier accounts for up to ca. 70% of the free-energy barrier to reaction. Nevertheless, rate differences for different phenols are largely due to differences in the activation energy, E(a,1) (range 2 to 10 kcal/mol). In phenols, electronic effects of the substituents and intramolecular H-bonds have a large influence on the activation energies and on the ArO-H BDEs. There is a linear Evans-Polanyi relationship between E(a,1) and the ArO-H BDEs: E(a,1)/kcal x mol(-1) = 0.918 BDE(ArO-H)/kcal x mol(-1) - 70.273. The proportionality constant, 0.918, is large and implies a "late" or "product-like" transition state (TS), a conclusion that is congruent with the small deuterium kinetic isotope effects (range 1.3-3.3). This Evans-Polanyi relationship, though questionable on theoretical grounds, has profitably been used to estimate several ArO-H BDEs. Experimental ArO-H BDEs are generally in good agreement with the DFT calculations. Significant deviations between experimental and DFT calculated ArO-H BDEs were found, however, when an intramolecular H-bond to the O(*) center was present in the phenoxyl radical, e.g., in ortho semiquinone radicals. In these cases, the coupled cluster with single and double excitations correlated wave function technique with complete basis set extrapolation gave excellent results. The TSs for the reactions of dpph(*) with phenol, 3- and 4-methoxyphenol, and 1,4-cyclohexadiene were also computed. Surprisingly, these TS structures for the phenols show that the reactions cannot be described as occurring exclusively by either a HAT or a PCET mechanism, while with 1,4-cyclohexadiene the PCET character in the reaction coordinate is much better defined and shows a strong pi-pi stacking interaction between the incipient cyclohexadienyl radical and a phenyl ring of the dpph(*) radical.     

Release of Formic Acid from Copper Formate: Hydride,Proton-Coupled Electron and Hydrogen Atom Transfer All Play their Role

Although the mechanism for the transformation of carbon dioxide to formate with copper hydride is well understood, it is not clear how formic acid is ultimately released. Herein, we show how formic acid is formed in the decomposition of the copper formate clusters Cu(II)(HCOO)₃⁻ and Cu(II)₂(HCOO)₅⁻. Infrared irradiation resonant with the antisymmetric C−O stretching mode activates the cluster, resulting in the release of formic acid and carbon dioxide. For the binary cluster, electronic structure calculations indicate that CO₂ is eliminated first, through hydride transfer from formate to copper. Formic acid is released via proton-coupled electron transfer (PCET) to a second formate ligand, evidenced by close to zero partial charge and spin density at the hydrogen atom in the transition state. Concomitantly, the two copper centers are reduced from Cu(II) to Cu(I). Depending on the detailed situation, either PCET or hydrogen atom transfer (HAT) takes place.     

Lone pair-pi and pi-pi interactions play an important role in proton-coupled electron transfer reactions

Proton-coupled electron transfer (PCET), a class of formal hydrogen atom transfer (HAT) reactions, is of widespread interest because it is implicated in a broad range of chemical and biochemical processes. PCET is typically differentiated from HAT by the fact that it occurs when a proton and electron are transferred between different sets of molecular orbitals. Previous theoretical work predicted that hydrogen bonding between reactants is a necessary but not sufficient condition for H exchanges to take place by PCET. This implies that HAT is the only mechanism for H exchange between two carbon atoms. In this work, we present computational results that show that the H exchange in the tert-butylperoxyl/phenol couple, a prototypical antioxidant exchange reaction, occurs by PCET and that the transfer of the electron can occur via an oxygen lone pair-ring pi overlap. We then show that the H exchange in a model for the tyrosyl/tyrosine couple, which is implicated in ribonucleotide reductase chemistry, occurs via PCET and that one path for the electron transfer is provided by a strong pi-stacking interaction. Finally, we show that a pi-stacking interaction in the benzyl/toluene couple, a system in which there is no H-bonding, can result in this exchange occurring via PCET to some extent. Collectively, these results indicate that PCET reactions are not unique to systems that can engage in H-bonding and that lone pair-pi and pi-pi interactions in these systems may be more important than previously understood.     

Mechanism for the Nonadiabatic Photooxidation of Benzene to Phenol: Orientation‐Dependent Proton‐Coupled Electron Transfer

An efficient catalytic one‐step conversion of benzene to phenol was achieved recently by selective photooxidation under mild conditions with 2,3‐dichloro‐5,6‐dicyano‐p‐benzoquinone (DDQ) as the photocatalyst. Herein, high‐level electronic structure calculations in the gas phase and in acetonitrile solution are reported to explore the underlying mechanism. The initially populated ¹ππ* state of DDQ can relax efficiently through a nearby dark ¹nπ* doorway state to the ³ππ* state of DDQ, which is found to be the precursor state involved in the initial intermolecular electron transfer from benzene to DDQ. The subsequent triplet‐state reaction between DDQ radical anions, benzene radical cations, and water is computed to be facile. The formed DDQH and benzene‐OH radicals can undergo T₁→S₀ intersystem crossing and concomitant proton‐coupled electron transfer (PCET) to generate the products DDQH₂ and phenol. Two of the four considered nonadiabatic pathways involve an orientation‐dependent triplet PCET process, followed by intersystem crossing to the ground state (S₀). The other two first undergo a nonadiabatic T₁→S₀ transition to produce a zwitterionic S₀ complex, followed by a barrierless proton transfer. The present theoretical study identifies novel types of nonadiabatic PCET processes and provides detailed mechanistic insight into DDQ‐catalyzed photooxidation.     

Pyrroles as antioxidants: solvent effects and the nature of the attacking radical on antioxidant activities and mechanisms of pyrroles, dipyrrinones, and bile pigments

The absolute rate constants, k(inh), and stoichiometric factors, n, of pyrroles, 2-methyl-3-ethylcarboxy-4,5-di-p-methoxyphenylpyrrole, 6, 2,3,4,5-tetraphenylpyrrole, 7, and 2,3,4,5-tetra-p-methoxyphenylpyrrole, 8, compared to the phenolic antioxidant, di-tert-butylhydroxyanisole, DBHA, during inhibited oxidation of cumene initiated by AIBN at 30 degrees C gave the relative antioxidant activities (k(inh)) DBHA > 8 > 7 > 6 and n = 2, whereas in styrene, 8 > DBHA. These results are explained by hydrogen atom transfer, HAT, from the N-H of pyrroles to ROO(*) radicals. The k(inh) values in styrene of dimethyl esters of the bile pigments of bilirubin ester (BRDE), of biliverdin ester (BVDE), and of a model compound (dipyrrinone, 1) gave k(inh) in the order pentamethylhydroxychroman (PMHC) > BRDE > 1 > BVDE. These antioxidant activities for BVDE and the model compound, 1, and PMHC dropped dramatically in the presence of methanol due to hydrogen bonding at the pyrrolic N-H group. In contrast the k(inh) of BRDE increased in methanol. We now show that pyrrolic compounds may react by HAT, proton-coupled electron transfer, PCET, or single electron transfer, SET, depending on their structure, the nature of the solvent, and the attacking radical. Compounds BVDE and 1 react by the HAT or PCET pathway (HAT/PCET) in styrene/chlorobenzene with ROO(*) and with the DPPH(*) radical in chlorobenzene according to N-H/N-D kH/kD of 1.6, whereas the DKIE with BRDE was only 1.2 with ROO(*). The antioxidant properties of polypyrroles of the BVDE class and model compounds (e.g., 1) are controlled by intramolecular H bonding which stabilizes an intermediate pyrrolic radical in HAT/PCET. According to kinetic polar solvent effects on the monopyrrole, 8, and BRDE, which gave increased rates in methanol, some pyrrolic structures are also susceptible to SET reactions. This conclusion is supported by some calculated ionization potentials. The antioxidant mechanism for BRDE with peroxyl radicals is described by the PCET reaction. Experiments using the 2,6-di-tert-butyl-4-(4'-methoxyphenyl)phenoxyl radical (DBMP(*)) showed this to be a better radical to monitor HAT activities in stopped-flow kinetics compared to the use of the more popular DPPH(*) radical.     

Role and effective treatment of dispersive forces in materials: Polyethylene and graphite crystals as test cases

A semiempirical addition of dispersive forces to conventional density functionals (DFT-D) has been implemented into a pseudopotential plane-wave code. Test calculations on the benzene dimer reproduced the results obtained by using localized basis set, provided that the latter are corrected for the basis set superposition error. By applying the DFT-D/plane-wave approach a substantial agreement with experiments is found for the structure and energetics of polyethylene and graphite, two typical solids that are badly described by standard local and semilocal density functionals.     

Proton-coupled electron transfer versus hydrogen atom transfer: generation of charge-localized diabatic states

The distinction between proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms is important for the characterization of many chemical and biological processes. PCET and HAT mechanisms can be differentiated in terms of electronically nonadiabatic and adiabatic proton transfer, respectively. In this paper, quantitative diagnostics to evaluate the degree of electron-proton nonadiabaticity are presented. Moreover, the connection between the degree of electron-proton nonadiabaticity and the physical characteristics distinguishing PCET from HAT, namely, the extent of electronic charge redistribution, is clarified. In addition, a rigorous diabatization scheme for transforming the adiabatic electronic states into charge-localized diabatic states for PCET reactions is presented. These diabatic states are constructed to ensure that the first-order nonadiabatic couplings with respect to the one-dimensional transferring hydrogen coordinate vanish exactly. Application of these approaches to the phenoxyl-phenol and benzyl-toluene systems characterizes the former as PCET and the latter as HAT. The diabatic states generated for the phenoxyl-phenol system possess physically meaningful, localized electronic charge distributions that are relatively invariant along the hydrogen coordinate. These diabatic electronic states can be combined with the associated proton vibrational states to generate the reactant and product electron-proton vibronic states that form the basis of nonadiabatic PCET theories. Furthermore, these vibronic states and the corresponding vibronic couplings may be used to calculate rate constants and kinetic isotope effects of PCET reactions.     

Solvent-modulated proton-coupled electron transfer in an iridium complex with an ESIPT ligand

Proton-coupled electron transfer (PCET), an essential process in nature with a well-known example of photosynthesis, has recently been employed in metal complexes to improve the energy conversion efficiency; however, a profound understanding of the mechanism of PCET in metal complexes is still lacking. In this study, we synthesized cyclometalated Ir complexes strategically designed to exploit the excited-state intramolecular proton transfer (ESIPT) of the ancillary ligand and studied their photoinduced PCET in both aprotic and protic solvent environments using femtosecond transient absorption spectroscopy and density functional theory (DFT) and time-dependent DFT calculations. The data reveal solvent-modulated PCET, where charge transfer follows proton transfer in an aprotic solvent and the temporal order of charge transfer and proton transfer is reversed in a protic solvent. In the former case, ESIPT from the enol form to the keto form, which precedes the charge transfer from Ir to the ESIPT ligand, improves the efficiency of metal-to-ligand charge transfer. This finding demonstrates the potential to control the PCET reaction in the desired direction and the efficiency of charge transfer by simply perturbing the external hydrogen-bonding network with the solvent.

The iridium complex with an ESIPT ligand shows solvent-modulated proton-coupled electron transfer, in which the temporal order of proton transfer and charge transfer is altered by the solvent environment.     

Modulation of Stacking Interactions by Transition‐Metal Coordination: Ab Initio Benchmark Studies

A series of ab initio calculations are used to determine the C? H???π and π???π‐stacking interactions of aromatic rings coordinated to transition‐metal centres. Two model complexes have been employed, namely, ferrocene and chromium benzene tricarbonyl. Benchmark data obtained from extrapolation of MP2 energies to the basis set limit, coupled with CCSD(T) correction, indicate that coordinated aromatic rings are slightly weaker hydrogen‐bond acceptors but are significantly stronger hydrogen‐bond donors than uncomplexed rings. It is found that π???π stacking to a second benzene is stronger than in the free benzene dimer, especially in the chromium case. This is assigned, by use of energy partitioning in the local correlation method, to dispersion interactions between metal d and benzene π orbitals. The benchmark data is also used to test the performance of more efficient theoretical methods, indicating that spin‐component scaling of MP2 energies performs well in all cases, whereas various density functionals describe some complexes well, but others with errors of more than 1 kcal mol^?1.     

Isolation of a Hydrogen‐Bonded Complex Based on the Anthranol/Anthroxyl Pair: Formation of a Hydrogen‐Atom Self‐Exchange System

A hydrogen‐bonded complex was successfully isolated as crystals from the anthranol/anthroxyl pair in the self‐exchange proton‐coupled electron transfer (PCET) reaction. The anthroxyl radical was stabilized by the introduction of a 9‐anthryl group at the carbon atom at the 10‐position. The hydrogen‐bonded complex with anthranol self‐assembled by π–π stacking to form a one‐dimensional chain in the crystal. The conformation around the hydrogen bond was similar to that of the theoretically predicted PCET activated complex of the phenol/phenoxyl pair. X‐ray crystal analyses revealed the self‐exchange of a hydrogen atom via the hydrogen bond, indicating the activation of the self‐exchange PCET reaction between anthranol and anthroxyl. Magnetic measurements revealed that magnetic ordering inside the one‐dimensional chain caused the inactivation of the self‐exchange reaction.     

Assessment of the pairwise additive approximation and evaluation of many-body terms for water clusters

We have tested the ability of four commonly used density functionals (three of which are semilocal and one of which is nonlocal) to outperform accurate pairwise additive approximations in the prediction of binding energies for a series of water clusters ranging in size from dimer to pentamer. Comparison to results obtained with the Weizmann-1 (W1) level of wave function theory shows that while all density functionals are capable of outperforming the accurate pairwise data, the choice of basis set used is crucial to the performance of the method, and if a poor choice of basis set is made the errors obtained with density functional theory (DFT) can be larger than those obtained with the simple pairwise approximation. We have also compared the binding energies and many-body terms determined with DFT to those obtained with W1, and have found that all semilocal functionals have significant errors in the many-body components of the full interactions energy. Despite this limitation, however, we have found that, of the four functionals tested, PBE1W/MG3S is the most accurate for predicting the binding energies of the clusters.     

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.     

Ab initio description of photoabsorption and electron transfer in a doubly-linked porphyrin-fullerene dyad

Structure, photoabsorption and excited states of two representative conformations obtained from molecular dynamics (MD) simulations of a doubly-linked porphyrin-fullerene dyad DHD6ee are studied by using both DFT and wavefunction based methods. Charge transfer from the donor (porphyrin) to the acceptor (fullerene) and the relaxation of the excited state are of special interest. The results obtained with LDA, GGA, and hybrid functionals (SVWN, PBE, and B3LYP, respectively) are analyzed with emphasis on the performance of used functionals as well as from the point of view of their comparison with wavefunction based methods (CCS, CIS(D), and CC2). Characteristics of the MD structures are retained in DFT optimization. The relative orientation of porphyrin and fullerene is significantly influencing the MO energies, the charge transfer (CT) in the ground state of the dyad and the excitation of ground state CT complex (g-CTC). At the same time, the excitation to the locally excited state of porphyrin is only little influenced by the orientation or cc distance. TD-DFT underestimates the excitation energy of the CT state, however for some cases (with relatively short donor-acceptor separations), the use of a hybrid functional like B3LYP alleviates the problem. Wavefunction based methods and CC2 in particular appear to overestimate the CT excitation energies but the inclusion of proper solvation models can significantly improve the results.