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At least 1,369 records · Page 76
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DOE OSTI2021

Permutationally Invariant Polynomial Expansions with Unrestricted Complexity

A general strategy is presented for constructing and validating permutationally invariant polynomial (PIP) expansions for chemical systems of any stoichiometry. Demonstrations are made for three categories of gas-phase dynamics and kinetics: collisional energy-transfer trajectories for predicting pressure-dependent kinetics, three-body collisions for describing transient van der Waals adducts relevant to atmospheric chemistry, and nonthermal reactivity via quasiclassical trajectories. In total, 30 systems are considered with up to 15 atoms and 39 degrees of freedom. Permutational invariance is enforced in PIP expansions with as many as 13 million terms and 13 permutationally distinct atom types by taking advantage of petascale computational resources. The quality of the PIP expansions is demonstrated through the systematic convergence of in-sample and out-of-sample errors with respect to both the number of training data and the order of the expansion, and these errors are shown to predict errors in the dynamics for both reactive and nonreactive applications. Here, the parallelized code distributed as part of this work enables the automation of PIP generation for complex systems with multiple channels and flexible user-defined symmetry constraints and for automatically removing unphysical unconnected terms from the basis set expansions, all of which are required for simulating complex reactive systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Accurate Free Energies for Complex Condensed-Phase Reactions Using an Artificial Neural Network Corrected DFTB/MM Methodology

Semiempirical methods like density functional tight-binding (DFTB) allow extensive phase space sampling, making it possible to generate free energy surfaces of complex reactions in condensed-phase environments. Such a high efficiency often comes at the cost of reduced accuracy, which may be improved by developing a specific reaction parametrization (SRP) for the particular molecular system. Thiol–disulfide exchange is a nucleophilic substitution reaction that occurs in a large class of proteins. Its proper description requires a high-level ab initio method, while DFT-GAA and hybrid functionals were shown to be inadequate, and so is DFTB due to its DFT-GGA descent. We develop an SRP for thiol–disulfide exchange based on an artificial neural network (ANN) implementation in the DFTB+ software and compare its performance to that of a standard SRP approach applied to DFTB. Furthermore, as an application, we use both new DFTB-SRP as components of a QM/MM scheme to investigate thiol–disulfide exchange in two molecular complexes: a solvated model system and a blood protein. Demonstrating the strengths of the methodology, highly accurate free energy surfaces are generated at a low cost, as the augmentation of DFTB with an ANN only adds a small computational overhead.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Integrated Quantum-Classical Protocol for the Realistic Description of Solvated Multinuclear Mixed-Valence Transition-Metal Complexes and Their Solvatochromic Properties

Linear cyanide-bridged polymetallic complexes, which undergo photoinduced metal-to-metal charge transfer, represent prototypical systems for studying long-range electron-transfer reactions and understanding the role played by specific solute–solvent interactions in modulating the excited-state dynamics. Here, to tackle this problem, while achieving a statistically meaningful description of the solvent and of its relaxation, one needs a computational approach capable of handling large polynuclear transition-metal complexes, both in their ground and excited states, as well as the ability to follow their dynamics in several environments up to nanosecond time scales. Here, we present a mixed quantum classical approach, which combines large-scale molecular dynamics (MD) simulations based on an accurate quantum mechanically derived force field (QMD-FF) and self-consistent QMD polarized point charges, with IR and UV–vis spectral calculations to model the solvation dynamics and optical properties of a cyano-bridged trinuclear mixed-valence compound (trans-[(NC) 5 Fe III (μ-CN)Ru II (pyridine) 4 (μ-NC)Fe III (CN) 5 ] 4– ). We demonstrate the reliability of the QMD-FF/MD approach in sampling the solute conformational space and capturing the local solute–solvent interactions by comparing the results with higher-level quantum mechanics/molecular mechanics (QM/MM) MD reference data. The IR spectra calculated along the classical MD trajectories in different solvents correctly predict the red shift of the CN stretching band in the aprotic medium (acetonitrile) and the subtle differences measured in water and methanol, respectively. By explicitly including the solvent molecules around the cyanide ligands and calculating the thermal averaged absorption spectra using time-dependent density functional theory calculations within the Tamm–Dancoff approximation, the experimental solvatochromic shift is quantitatively reproduced going from water to methanol, while it is overestimated for acetonitrile. This discrepancy can likely be traced back to the lack of important dispersion interactions between the solvent cyano groups and the pyridine substituents in our micro solvation model. The proposed protocol is applied to the ground state in water, methanol, and acetonitrile and can be flexibly generalized to study excited-state nonequilibrium solvation dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Atomic-Level Features for Kinetic Monte Carlo Models of Complex Chemistry from Molecular Dynamics Simulations

The high computational cost of evaluating atomic interactions recently motivated the development of computationally inexpensive kinetic models, which can be parametrized from MD simulations of complex chemistry of thousands of species or other processes and accelerate the prediction of the chemical evolution by up to four order of magnitude. Such models go beyond the commonly employed potential energy surface fitting methods in that they are aimed purely at describing kinetic effects. So far, such kinetic models utilize molecular descriptions of reactions and have been constrained to only reproduce molecules previously observed in MD simulations. Therefore, these descriptions fail to predict the reactivity of unobserved molecules, for example in the case of large molecules or solids. In this work, we propose a new approach for the extraction of reaction mechanisms and reaction rates from MD simulations, namely the use of atomic-level features. Using the complex chemical network of hydrocarbon pyrolysis as example, it is demonstrated that kinetic models built using atomic features are able to explore chemical reaction pathways never observed in the MD simulations used to parametrize them, a critical feature to describe rare events. Atomic-level features are shown to construct reaction mechanisms and estimate reaction rates of unknown molecular species from elementary atomic events. Through comparisons of the model ability to extrapolate to longer simulation timescales and different chemical compositions than the ones used for parameterization, it is demonstrated that kinetic models employing atomic features retain the same level of accuracy and transferability as the use of features based on molecular species, while being more compact and parametrized with less data. We also find that atomic features can better describe the formation of large molecules enabling the simultaneous description of small molecules and condensed phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Excited-State Bond Contraction and Charge Migration in a Platinum Dimer Complex Characterized by X-ray and Optical Transient Absorption Spectroscopy

Interactions between metal centers in dimeric transition metal complexes (TMCs) play important roles in their excited-state energetics and pathways, and, thus, affect their photophysical properties relevant to their applications, e.g., photoluminescent materials and photocatalysis. In this study, we report electronic and nuclear structural dynamics studies of two photoexcited pyrazolate-bridged [Pt(ppy)(µ-R 2 pz)] 2 -type Pt(II) dimers (ppy = 2-phenylpyridine, µ-R 2 pz = 3,5-substituted pyrazolate): [Pt(ppy)(µ-H 2 pz)] 2 (1) and [Pt(NDI-ppy)(µ-Ph 2 pz)] 2 (2, NDI = 1,4,5,8-naphthalenediimide), both of which have distinct ground state Pt-Pt distances. X-ray transient absorption spectroscopy at the Pt L III -edge revealed a new d-orbital vacancy due to the one-electron oxidation of the Pt centers in 1 and 2. However, while a transient Pt-Pt contraction was observed in 2, such an effect was completely absent in 1, demonstrating how the excited states of these complexes are determined by the overlap of the Pt (d z 2 ) orbitals, which is tuned by steric bulk of the pyrazolate R-groups in the 3- and 5-positions. In tandem with analysis of the Pt-Pt distance structural parameter, we observed photoinduced charge separation in 2 featuring a covalently linked NDI acceptor on the ppy ligand. The formation and subsequent decay of the NDI radical anion absorption signals were detected upon photoexcitation using optical transient absorption spectroscopy. The NDI radical anion decayed on the same timescale, hundreds of picoseconds, as that of the d-orbital vacancy signal of the oxidized Pt-Pt core observed in the XTA measurements. The data indicated ultrafast formation of the charge-separated state and subsequent charge recombination to the original Pt(II-II) species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Two-Color IRMPD Applied to Conformationally Complex Ions: Probing Cold Ion Structure and Hot Ion Unfolding

Two-color infrared multiphoton dissociation (2C-IRMPD) spectroscopy is a technique that mitigates spectral distortions due to nonlinear absorption that is inherent to one-color IRMPD. We use a 2C-IRMPD scheme that incorporates two independently tunable IR sources, providing considerable control over the internal energy content and type of spectrum obtained by varying the trap temperature, the time delays and fluences of the two infrared lasers, and whether the first or second laser wavelength is scanned. In this work, we describe the application of this variant of 2C-IRMPD to conformationally complex peptide ions. The 2C-IRMPD technique is used to record near-linear action spectra of both cations and anions with temperatures ranging from 10 to 300 K. In this work, we also determine the conditions under which it is possible to record IR spectra of single conformers in a conformational mixture. Furthermore, we demonstrate the capability of the technique to explore conformational unfolding by recording IR spectra with widely varying internal energy in the ion. The protonated peptide ions YGGFL (NH 3 + -Tyr-Gly-Gly-Phe-Leu, Leu-enkephalin) and YGPAA (NH 3 + -Tyr-Gly-Pro-Ala-Ala) are used as model systems for exploring the advantages and disadvantages of the method when applied to conformationally complex ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Interplay of Electronic and Geometric Structure Tunes Organic Biradical Character in Bimetallic Tetrathiafulvalene Tetrathiolate Complexes

The synthesis and design of organic biradicals with tunable singlet–triplet gaps have become the subject of significant research interest, owing to their possible photochemical applications and use in the development of molecular switches and conductors. Recently, tetrathiafulvalene tetrathiolate (TTFtt) has been demonstrated to exhibit such organic biradical character in doubly ionized bimetallic complexes. In this article we use high-level ab initio calculations to interrogate the electronic structure of a series of TTFtt-bridged metal complexes, resolving the factors governing their biradical character and singlet–triplet gaps. Here, we show that the degree of biradical character correlates with a readily measured experimental predictor, the central TTFtt C–C bond length, and that it may be described by a one-parameter model, providing valuable insight for the future rational design of TTFtt based biradical compounds and materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Bridge-Mediated Metal-to-Metal Electron and Hole Transfer in a Supermolecular Dinuclear Complex: A Computational Study Using Quantum Electron–Nuclear Dynamics

Bimetallic electron donor–acceptor complexes can facilitate electron and energy transfer with excellent structural control through synthetic design. In this work, we investigate the photochemical dynamics in a Ru–Cu bimetallic complex after photoexcitation of the Ru-centered charge transfer state. The physical underpinnings of the metal-to-metal directional charge transfer process are unraveled via analyses of the quantum electronic dynamics and electron–nuclear trajectories. Here, the effects of molecular vibrations in the photoexcited state on the charge transfer processes are also analyzed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Importance of Dispersion in the Molecular Geometries of Mn(III) Spin-Crossover Complexes

The computational investigation of the molecular geometries of a pair of manganese(III) spin-crossover complexes is reported. For the geometry of the quintet high-spin state, density functionals significantly overestimate Mn–Namine bond distances, although the geometry for the triplet intermediate-spin state is well described. Here, comparisons with several wave function-based methods demonstrate that this error is due to the limited ability of commonly used density functionals to recover dispersion beyond a certain extent. Among the methods employed for geometry optimization, restricted open-shell Møller–Plesset perturbation theory (MP2) appropriately describes the high-spin geometry but results in a slightly shorter Mn–O distance in both spin states. On the other hand, extended multistate complete active space second-order perturbation theory (XMS-CASPT2) provides a good description of the geometry for the intermediate-spin state but also sufficiently recovers dispersion, performing well for the high-spin state. Despite the fact that the electronic structure of both spin states is dominated by one-electron configuration, XMS-CASPT2 offers a balanced approach, leading to molecular geometries with much better agreement with experiment than MP2 and DFT. A scan along the Mn–N amine bond demonstrates that for these complexes coupled cluster methods (i.e., DLPNO-CCSD(T)) also yield bond distances in agreement with experiment while multiconfiguration pair density functional theory (MC-PDFT) is unable to recover dispersion well enough, analogous to single-reference DFT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Threshold Collision-Induced Dissociation of Hydrated Thorium(IV) Trihydroxide Cation: Experimental and Theoretical Investigation of the Binding Energies for Th(OH) 3 + (H 2 O) n Complexes ( n = 1–4)

Threshold collision-induced dissociation of Th(OH) 3 + (H 2 O) n Complexes ( n = 1–4) with xenon was performed using a guided ion beam tandem mass spectrometer. The primary dissociation pathway for all complexes is a loss of a single water molecule followed by the sequential loss of additional water molecules at higher collision energies. Here, the data were analyzed using a statistical model after accounting for lifetime effects and reactant internal and kinetic energy distributions to obtain 0 K bond dissociation energies (BDEs). These were also converted using rigid rotor/harmonic oscillator approximations to yield thermodynamic values at room temperature. The 0 K BDEs of H 2 O ligands to Th(OH) 3 + (IV) are experimentally determined for the first time as 106 ± 6, 89 ± 6, 76 ± 4, and 51 ± 4 kJ/mol for the first, second, third, and fourth water ligand added. These values agree reasonably well with values calculated at the B3LYP, B3PW91, and PBE0 levels of theory with aug-cc-pVQZ basis sets, whereas B3LYP-GD3BJ, MP2, and CCSD(T) single point energies with (without) counterpoise corrections systematically overestimate the bond energies by about 15 (20), 19 (25), and (18) kJ/mol, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

Here, we analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call “complexity reduction”. In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature T g of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2–6 nm at T g . Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

cancer↗
DOE OSTI2020

Local Atomic Structure in Photo-isomerized Ruthenium Sulfur Dioxide Complexes Revealed by Pair Distribution Function Analysis

SO 2 linkage photoisomerization in crystalline ruthenium-based complexes has demonstrated nanophotonic phenomena such as optical switching and nano-optomechanical transduction. Molecular insights into these materials have been explored largely via the characterization of their photoinduced crystal structures via in situ single-crystal X-ray diffraction, known as photocrystallography. Photoinduced molecular disorder is present, which photocrystallography can model to the extent that it is confined within the periodic boundary of a unit cell. However, non-periodic molecular disorder is suspected to exist as well. In situ total scattering experiments were therefore carried out on finely powdered crystals of four ruthenium-sulfur dioxide complexes. Data were modeled using light-minus-dark' difference pair distribution function analysis, which afforded photoinduced structural changes exclusively. This revealed structural features that were first compared against models of photoinduced crystal structures known a priori from photocrystallography. Furthermore, statistical inference was then employed, which evidenced generally good agreement between the total scattering data and the photocrystallographic models, while revealing real differences that are indicative of a structure with only a short-range order. Overall, our findings demonstrate that in situ light-induced total scattering experiments on finely powdered crystals are able to reveal the photoinduced structure. Overall, the evidence suggests that such structure could include a short-range order as well as photocrystallographic content. Our demonstration experiment offers a pathway to develop studies that capture the short-range order in linkage photoisomers, while we have outlined the procedure for testing the validity of associated structural models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Pressure-Stabilized MnSb2 with Complex Incommensurate Magnetic Order

Marcasite-type compounds have been proposed as promising hosts of exotic magnetic quantum states, yet experimental realizations in stoichiometric, disorder-free systems remain limited. Here, we report the high-pressure stabilization and magnetic characterization of MnSb2, a marcasite-type compound that is thermodynamically metastable under ambient pressure. Single crystals were synthesized using a cubic multianvil press at 3.3 GPa and 490 °C for 24 h, and powder and single-crystal X-ray diffraction confirm the orthorhombic Pnnm structure. These crystals are stable at ambient pressure for a long time up to between 450 and 500 K. Heat-capacity measurements reveal phase transitions at approximately T0 ∼ 118 K and T1 ∼ 220 K. Neutron diffraction uncovers an unconventional magnetic state below T1 ∼ 220 K. Magnetic powder neutron diffraction refinements reveal possible multiple magnetic configurations that provide comparably acceptable fits to the experimental data. While most solutions are consistent with a spin-density-wave (SDW) description, helical models systematically yield inferior agreement factors. Across a broad range of models, the Mn ordered moment reaches a maximum value of approximately 2 μB and remains predominantly collinear, with minimal canting along the c-axis. At 200 K, the magnetic propagation vector is q = (0, 0.3975, 0.3783); upon cooling, the b component increases toward 0.5, reflecting a temperature-dependent evolution of the modulation. The need for modification of the magnetic model between high and low temperatures further highlights the complex and strongly temperature-dependent nature of the magnetic order in this system. These results establish MnSb2 as a pressure-stabilized marcasite magnet with a tunable, complex magnetic state and a compelling stoichiometric platform for exploring unconventional magnetic behavior, including potential altermagnetism.

Xu, Mingyu [Michigan State University , , , ,; Iow↗
DOE OSTI2020

Exploiting Machine Learning to Efficiently Predict Multidimensional Optical Spectra in Complex Environments

The excited-state dynamics of chromophores in complex environments determine a range of vital biological and energy capture processes. Time-resolved, multidimensional optical spectroscopies provide a key tool to investigate these processes. Although theory has the potential to decode these spectra in terms of the electronic and atomistic dynamics, the need for large numbers of excited-state electronic structure calculations severely limits first-principles predictions of multidimensional optical spectra for chromophores in the condensed phase. In this work, we leverage the locality of chromophore excitations to develop machine learning models to predict the excited-state energy gap of chromophores in complex environments for efficiently constructing linear and multidimensional optical spectra. By analyzing the performance of these models, which span a hierarchy of physical approximations, across a range of chromophore–environment interaction strengths, we provide strategies for the construction of machine learning models that greatly accelerate the calculation of multidimensional optical spectra from first principles.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Charge-Transfer Luminescence in a Molecular Donor–Acceptor Complex: Computational Insights

Donor–acceptor molecular complexes are a popular class of materials utilizing charge-transfer states for practical applications. A recent class of donor–acceptor dyads based on the fluorescent BODIPY functionalized with triphenylamine (TPA) shows the peculiar property of dual fluorescence. It is hypothesized that instead of the sensitized charge-transfer state being optically dark, it provides an additional bright radiative pathway. In this study, we use time-dependent density functional theory to characterize the energetic alignment of excitonic and charge-transfer states in a BODIPY-TPA molecular complex. We observe that using a long-range exchange corrected functional in combination with state-specific solvation scheme gives a qualitatively correct alignment of the exciton and charge-transfer states and an enhancement in oscillator strength for the equilibrium solvated charge-transfer state, in agreement with experiment. Furthermore, this work provides rationalization of charge-transfer state emission and provides a foundation to explore charge-transfer using ab initio excited-state nonadiabatic dynamics.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Beyond Duality: Rationalizing Repulsive Coulomb Barriers in Host–Guest Cyclodextrin–Dodecaborate Complexes

The repulsive Coulomb barrier (RCB), an intrinsic potential energy barrier along electron detachment or charge-separation coordinates in multiply charged anions (MCAs), provides dynamic stability to MCAs whose electronic and thermodynamic stabilities are largely dictated by strong internal Coulomb repulsions. Spectroscopic and theoretical characterizations of the RCB have been focused on isolated MCAs. In this work, we extend the RCB investigation beyond the previous scope by including noncovalent host–guest cyclodextrin-closo-dodecaborate dianionic complexes χCD·B 12 X 12 2– (χ = α, β, γ; X = H, F–I). Here, photodechment photoelectron spectroscopy reveals the existence of two distinctly different RCBs, derived from detaching electrons from the guest dianions (RCB 1 ) or ionizing the host neutrals (RCB 2 ), respectively, with the latter being substantially smaller than the former. In conclusion, theoretical calculations support the duality of RCBs in these complexes and further exhibit highly anisotropic nature of the RCBs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Probing Complex Chemical Processes at the Molecular Level with Vibrational Spectroscopy and X-ray Tools

Understanding the origins of structure and bonding at the molecular level in complex chemical systems spanning magnitudes in length and time is of paramount interest in physical chemistry. Here, we have coupled vibrational spectroscopy and X-ray based techniques with a series of microreactors and aerosol beams to tease out intricate and sometimes subtle interactions, such as hydrogen bonding, proton transfer, and noncovalent interactions. This allows for unraveling the self-assembly of arginine-oleic acid complexes in an aqueous solution and growth processes in a metal–organic framework. Terahertz and infrared spectroscopy provide an intimate view of the hydrogen-bond network and associated phase changes with temperature in neopentyl glycol. The hydrogen-bond network in aqueous glycerol aerosols and levels of protonation of nicotine in aqueous aerosols are visualized. Future directions in probing the hydrogen-bond networks in deep eutectic solvents and organic frameworks are described, and we suggest how X-ray scattering coupled to X-ray spectroscopy can offer insight into the reactivity of organic aerosols.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Deciphering Charge Transfer Processes in Transition Metal Complexes from the Perspective of Ultrafast Electronic and Nuclear Motions

Chemical transformations in charge transfer states result from the interplay between electronic dynamics and nuclear reorganization along excited-state trajectories. Here, in this study, we investigate the ultrafast structural dynamics following photoinduced electron transfer from the metal-metal-to-ligand charge transfer state of an electron donor, a Pt dimer complex, to a covalently linked electron acceptor group using ultrafast time-resolved wide-angle X-ray scattering and optical transient absorption spectroscopy methods to disentangle the interdependence of the excited-state electronic and nuclear dynamics. Following photoexcitation, Pt-Pt bond formation and contraction takes up to 1 ps, much slower than the corresponding process in analogous complexes without electron acceptor groups. Because the Pt-Pt distance change is slow with respect to excited-state electron transfer, it can affect the rate of electron transfer. These results have potential impacts on controlling electron transfer rates via structural alterations to the electron donor group, tuning the charge transfer driving force.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗