Calculation Of Electron Transfer Rates Research Articles

Photocatalytic Reduction of CO2 to HCOOH and CO by a Phosphine-Bipyridine-Phosphine Ir(III) Catalyst: Photophysics, Nonadiabatic Effects, Mechanism, and Selectivity.

Photocatalytic CO2 reduction is one of the best solutions to solve the global energy crisis and to realize carbon neutralization. The tetradentate phosphine-bipyridine (bpy)-phosphine (PNNP)-type Ir(III) photocatalyst, Mes-IrPCY2, was reported with a high HCOOH selectivity but the photocatalytic mechanism remains elusive. Herein, we employ electronic structure methods in combination with radiative, nonradiative, and electron transfer rate calculations, to explore the entire photocatalytic cycle to either HCOOH or CO, based on which a new mechanistic scenario is proposed. The catalytic reduction reaction starts from the generation of the precursor metal-to-ligand charge transfer (3 MLCT) state. Subsequently, the divergence happens from the 3 MLCT state, the single electron transfer (SET) and deprotonation process lead to the formation of one-electron-reduced species and Ir(I) species, which initiate the reduction reaction to HCOOH and CO, respectively. Interestingly, the efficient occurrence of proton or electron transfer reduces barriers of critical steps. In addition, nonadiabatic transitions play a nonnegligible role in the cycle. We suggest a lower free-energy barrier in the reaction-limiting step and the very efficient SET in 3 MLCT are cooperatively responsible for a high HCOOH selectivity. The gained mechanistic insights could help chemists to understand, regulate, and design photocatalytic CO2 reduction reaction of similar function-integrated molecular photocatalyst.

Photocatalytic Reduction of CO2 to HCOOH and CO by a Phosphine‐Bipyridine‐Phosphine Ir(III) Catalyst: Photophysics, Nonadiabatic Effects, Mechanism, and Selectivity

AbstractPhotocatalytic CO2 reduction is one of the best solutions to solve the global energy crisis and to realize carbon neutralization. The tetradentate phosphine‐bipyridine (bpy)‐phosphine (PNNP)‐type Ir(III) photocatalyst, Mes‐IrPCY2, was reported with a high HCOOH selectivity but the photocatalytic mechanism remains elusive. Herein, we employ electronic structure methods in combination with radiative, nonradiative, and electron transfer rate calculations, to explore the entire photocatalytic cycle to either HCOOH or CO, based on which a new mechanistic scenario is proposed. The catalytic reduction reaction starts from the generation of the precursor metal‐to‐ligand charge transfer (3MLCT) state. Subsequently, the divergence happens from the 3MLCT state, the single electron transfer (SET) and deprotonation process lead to the formation of one‐electron‐reduced species and Ir(I) species, which initiate the reduction reaction to HCOOH and CO, respectively. Interestingly, the efficient occurrence of proton or electron transfer reduces barriers of critical steps. In addition, nonadiabatic transitions play a nonnegligible role in the cycle. We suggest a lower free‐energy barrier in the reaction‐limiting step and the very efficient SET in 3MLCT are cooperatively responsible for a high HCOOH selectivity. The gained mechanistic insights could help chemists to understand, regulate, and design photocatalytic CO2 reduction reaction of similar function‐integrated molecular photocatalyst.

Direct Calculation of Electron Transfer Rates with the Binless Dynamic Histogram Analysis Method.

Umbrella sampling molecular dynamics simulations are widely used to enhance sampling along the reaction coordinates of chemical reactions. The effect of the artificial bias can be removed using methods such as the dynamic weighted histogram analysis method (DHAM), which in addition to the global free energy profile also provides kinetic information about barrier-crossing rates directly from the Markov matrix. Here we present a binless formulation of DHAM that extends DHAM to high-dimensional and Hamiltonian-based biasing to allow the study of electron transfer (ET) processes, for which enhanced sampling is usually not possible based on simple geometric grounds. We show the capabilities of binless DHAM on examples such as aqueous ferrous-ferric ET and intramolecular ET in the radical anion of benzoquinone-tetrathiafulvalene-benzoquinone (Q-TTF-Q)-. From classical Hamiltonian-based umbrella sampling simulations and electronic coupling values from quantum chemistry calculations, binless DHAM provides ET rates for adiabatic and nonadiabatic ET reactions alike in excellent agreement with experimental results.

Semiclassical instanton formulation of Marcus-Levich-Jortner theory.

Marcus-Levich-Jortner (MLJ) theory is one of the most commonly used methods for including nuclear quantum effects in the calculation of electron-transfer rates and for interpreting experimental data. It divides the molecular problem into a subsystem treated quantum-mechanically by Fermi's golden rule and a solvent bath treated by classical Marcus theory. As an extension of this idea, we here present a "reduced" semiclassical instanton theory, which is a multiscale method for simulating quantum tunneling of the subsystem in molecular detail in the presence of a harmonic bath. We demonstrate that instanton theory is typically significantly more accurate than the cumulant expansion or the semiclassical Franck-Condon sum, which can give orders-of-magnitude errors and, in general, do not obey detailed balance. As opposed to MLJ theory, which is based on wavefunctions, instanton theory is based on path integrals and thus does not require solutions of the Schrödinger equation nor even global knowledge of the ground- and excited-state potentials within the subsystem. It can thus be efficiently applied to complex, anharmonic multidimensional subsystems without making further approximations. In addition to predicting accurate rates, instanton theory gives a high level of insight into the reaction mechanism by locating the dominant tunneling pathway as well as providing similar information to MLJ theory on the bath activation energy and the vibrational excitation energies of the subsystem states involved in the reaction.

Extension of instanton theory includes tunneling effects in electron transfer rate calculations

Tunneling effects lead to large discrepancies in electron transfer rate calculations in the Marcus inverted regime.

A Hybrid Quantum Mechanical Approach: Intimate Details of Electron Transfer between Type-I CdSe/ZnS Quantum Dots and an Anthraquinone Molecule.

We report a hybrid computational approach to calculate electron transfer between a type-I CdSe/ZnS core/shell quantum dot (QD) with a varying shell thickness and the functionalized anthraquinone (AQ) molecule. This novel approach combines the traditional electron/hole confinement theory in the effective mass approximation for the QD and molecular orbital theory for the AQ molecule. In the present study, the QD's electron and hole envelope wave functions are solutions of the effective-mass Schrödinger equation, and the AQ wave function is obtained at the density functional level. Electron-transfer rate calculations are based on Marcus's theory with the coupling strength computed according to an one-electron orbital perturbation model. We show that in a heptane solution, the LUMO of AQ and the 1Se electron orbital of QD are involved in the charge separation (CS) process. The charge recombination (CR) process, on the other hand, occurs from the singly occupied molecular orbital of the AQ radical (which corresponds to the LUMO in AQ) to a trapped hole state of the QD within the band gap. The calculations support previously reported interpretations of the role of the ZnS shell as a hindrance in the CS and CR process.

Calculation of electron transfer rates in proteins

Electron transfer rates in Zn/Ru modified myoglobins are calculated using a molecular orbital method to obtain the electronic factor and empirical values of the reorganization energy and driving force. The protein is partitioned into three subsystems, A, B, and C, where A and C consist of the metal ions and their ligands and B is the protein bridge between A and C. Molecular orbitals are calculated in each subsystem. Interaction matrix elements between the subsystems are calculated and the total eigenvalue problem solved using a partitioning technique. The distance dependence of the rate is only roughly exponential as a function of intermetal distance. In particular, the rate of the His-12 derivative is larger than the average exponential decrease, in agreement with the experiments. If the indole group in the pathway between the metal ions is replaced by an equally large (CH{sub 2})n-chain, the calculated rate is close to the average exponential decrease. The electronic spectra of zinc porphin (ZnP) and Zn-substituted myoglobin (ZnMb) are calculated using a CNDO/S approach, and the results compare favorably with the corresponding experimental spectra.

Structure of a Xanthine Oxidase-Related 4-Hydroxybenzoyl-CoA Reductase with an Additional [4Fe-4S] Cluster and an Inverted Electron Flow

The Mo-flavo-Fe/S-dependent heterohexameric protein complex 4-hydroxybenzoyl-CoA reductase (4-HBCR, dehydroxylating) is a central enzyme of the anaerobic degradation of phenolic compounds and belongs to the xanthine oxidase (XO) family of molybdenum enzymes. Its X-ray structure was established at 1.6 A resolution. The most pronounced difference between 4-HBCR and other structurally characterized members of the XO family is the insertion of 40 amino acids within the beta subunit, which carries an additional [4Fe-4S] cluster at a distance of 16.5 A to the isoalloxazine ring of FAD. The architecture of 4-HBCR and concomitantly performed electron transfer rate calculations suggest an inverted electron transfer chain from the donor ferredoxin via the [4Fe-4S] cluster to the Mo over a distance of 55 A. The binding site of 4-hydroxybenzoyl-CoA is located in an 18 A long channel lined up by several aromatic side chains around the aromatic moiety, which are proposed to shield and stabilize the postulated radical intermediates during catalysis.

Failure of the Born–Oppenheimer and Franck–Condon approximations for long distance electron transfer rate calculations

Quantum mechanical and semiclassical formulations of nonadiabatic electron transfer theory are usually implemented within a Born–Oppenheimer regime. Calculations on real weakly interacting systems are so difficult that this approximation is rarely questioned. The Born–Oppenheimer approximation becomes qualitatively wrong for electron transfers at very large distances. A model vibronic problem is exactly solved and compared with the Born–Oppenheimer result. Rate expressions are derived from the wave functions using the ‘‘golden rule’’ approximation. Electron propagation is intimately correlated to nuclear motion so that the vibrational energy left on the donor critically affects the electronic decay length. Several deviations from the usual predictions appear for transfers over very large distances.

Ab initio calculation of electron transfer rates in a model of the metal-electrolyte interface

We present calculations of the rate of electron transfer from a semi-infinite jellium metal to a proton imbedded in a polarizable insulating medium. The model is interpreted to give values of the slope of the voltage-log current characteristic of a metal-electrolyte interface. We use a form of the local density approximation to the Kohn-Sham local density variational technique, so that the model contains the quantum properties of the interacting electron gas.

Ab initio calculation of electron transfer rates in a model of the metal-electrolyte interface

We present calculations of the rate of electron transfer from a semi-infinite jellium metal to a proton imbedded in a polarizable insulating medium. The model is interpreted to give values of the slope of the voltage-log current characteristic of a metal-electrolyte interface. We use a form of the local density approximation to the Kohn-Sham local density variational technique, so that the model contains the quantum properties of the interacting electron gas.

Intramolecular electron transfer in simple model systems: A propagator study

The probability of site-to-site intramolecular electron or hole transfer as a function of time in simple model systems is calculated. Systems studied are the hydrogen molecule, allyl cation, and cyclopropenium ion, in the Hubbard model. We employ the method of electron propagators, using both exact and approximate (molecular orbital and valence bond) ground state wavefunctions. We conclude that the molecular orbital wavefunction affords a good description of the transfer process for a wide variety of systems. The utility of our approach for the calculation of electron transfer rates in which purely electronic effects are dominant is stressed.