Kinetic isotope effects in chemical and biochemical reactions: physical basis and theoretical methods of calculation

Reactions dynamics for X + H2 insertion reactions (X = C(1D), N(2D), O(1D), S(1D)) with Cayley propagator ring-polymer molecular dynamics

In this work, rate coefficients of four prototypical insertion reactions, X + H2 → H + XH (X = C(1D), N(2D), O(1D), S(1D)), and associated isotope reactions are calculated based on ring polymer molecular dynamics (RPMD) with Cayley propagator (Cayley-RPMD). The associated kinetic isotope effects are systematically studied too. The Cayley propagator used in this work increases the stability of numerical integration in RPMD calculations and also supports a larger evolution time interval, allowing us to reach both high accuracy and efficiency. So, our results do not only provide chemical kinetic data for the title reactions in an extended temperature range but also consist of experimental results, standard RPMD, and other theoretical methods. The results in this work also reflect that Cayley-RPMD has strong consistency and high reliability in its investigations of chemical dynamics for insertion reactions.

The Conductance Isotope Effect in Oligophenylene Imine Molecular Wires Depends on the Number and Spacing of 13C-Labeled Phenylene Rings

We report a strong and structurally sensitive 13C intramolecular conductance isotope effect (CIE) for oligophenyleneimine (OPI) molecular wires connected to Au electrodes. Wires were built from Au surfaces beginning with the formation of 4-aminothiophenol self-assembled monolayers (SAMs) followed by subsequent condensation reactions with 13C-labeled terephthalaldehyde and phenylenediamine; in these monomers the phenylene rings were either completely 13C-labeled or the naturally abundant 12C isotopologues. Alternatively, perdeuterated versions of terephthalaldehyde and phenylenediamine were employed to make 2H(D)-labeled OPI wires. For 13C-isotopologues of short OPI wires (<4 nm) in length where the charge transport mechanism is tunneling, there was no measurable effect, i.e., 13C CIE ≈ 1, where CIE is defined as the ratio of labeled and unlabeled wire resistances, i.e., CIE = Rheavy/Rlight. However, for long OPI wires >4 nm, in which the transport mechanism is polaron hopping, a strong 13C CIE = 4-5 was observed. A much weaker inverse CIE < 1 was evident for the longest D-labeled wires. Importantly, the magnitude of the 13C CIE was sensitive to the number and spacing of 13C-labeled rings, i.e., the CIE was structurally sensitive. The structural sensitivity is intriguing because it may be employed to understand polaron hopping mechanisms and charge localization/delocalization in molecular wires. A preliminary theoretical analysis explored several possible explanations for the CIE, but so far a fully satisfactory explanation has not been identified. Nevertheless, the latest results unambiguously demonstrate structural sensitivity of the heavy atom CIE, offering directions for further utilization of this interesting effect.

Estimation of frequency factors for the calculation of kinetic isotope effects from classical and path integral free energy simulations

We use the modified Bigeleisen-Mayer equation to compute kinetic isotope effect values for non-enzymatic phosphoryl transfer reactions from classical and path integral molecular dynamics umbrella sampling. The modified form of the Bigeleisen-Mayer equation consists of a ratio of imaginary mode vibrational frequencies and a contribution arising from the isotopic substitution's effect on the activation free energy, which can be computed from path integral simulation. In the present study, we describe a practical method for estimating the frequency ratio correction directly from umbrella sampling in a manner that does not require normal mode analysis of many geometry optimized structures. Instead, the method relates the frequency ratio to the change in the mass weighted coordinate representation of the minimum free energy path at the transition state induced by isotopic substitution. The method is applied to the calculation of 16/18O and 32/34S primary kinetic isotope effect values for six non-enzymatic phosphoryl transfer reactions. We demonstrate that the results are consistent with the analysis of geometry optimized transition state ensembles using the traditional Bigeleisen-Mayer equation. The method thus presents a new practical tool to enable facile calculation of kinetic isotope effect values for complex chemical reactions in the condensed phase.

Accurate Single-Molecule Kinetic Isotope Effects

An accurate single-molecule kinetic isotope effect (sm-KIE) was applied to circumvent the inherent limitation of conventional ensemble KIE by using graphene-molecule-graphene single-molecule junctions. In situ monitoring of the single-molecule reaction trajectories in real time with high temporal resolution has the capability to characterize the deeper information brought by KIE. The C-O bond cleavage and the C-C bond formation of the transition state (TS) were observed in the Claisen rearrangement through the secondary kinetic isotope effect, demonstrating the high detection sensitivity and accuracy of this method. More interestingly, this sm-KIE can be used to determine TS structures under different electric fields, revealing the multidimensional regulation of the TS. The detection and manipulation of the TS provide a broad perspective to understand and optimize chemical reactions and biomimetic progress.

Heavy-Atom Kinetic Isotope Effects: Primary Interest or Zero Point?

Chemists have many options for elucidating reaction mechanisms. Global kinetic analysis and classic transition-state probes (e.g., LFERs, Eyring) inevitably form the cornerstone of any strategy, yet their application to increasingly sophisticated synthetic methodologies often leads to a wide range of indistinguishable mechanistic proposals. Computational chemistry provides powerful tools for narrowing the field in such cases, yet wholly simulated mechanisms must be interpreted with great caution. Heavy-atom kinetic isotope effects (KIEs) offer an exquisite but underutilized method for reconciling the two approaches, anchoring the theoretician in the world of calculable observables and providing the experimentalist with atomistic insights. This Perspective provides a personal outlook on this synergy. It surveys the computation of heavy-atom KIEs and their measurement by NMR spectroscopy, discusses recent case studies, highlights the intellectual reward that lies in alignment of experiment and theory, and reflects on the changes required in chemical education in the area.

Large Anharmonic Effects on Tunneling and Kinetics: Reaction of Propane with Muonium

Calculations of kinetic isotope effects (KIEs) provide challenging tests of quantal mass effects on reaction rates, and muonium KIEs are the most challenging. Here, we show that it can be very important to include reaction-coordinate-dependent vibrational anharmonicity along the whole reaction path to calculate tunneling probabilities and KIEs. For the reaction of propane with Mu, this decreases both the height and width of the vibrationally adiabatic potential barrier, with both effects increasing the rate constants. Our results agree well with the experimental observations.

Kinetic Isotope Effect as a Tool To Investigate the Oxygen Reduction Reaction on Pt-based Electrocatalysts - Part II: Effect of Platinum Dispersion

We investigated the oxygen reduction reaction (ORR) mechanism on Pt nanoparticles (NPs) dispersed on several carbon blacks with various physicochemical properties (i. e. specific surface ranging from 80 to 900 m²  g^-1 , different graphitization degree, etc.). Using the kinetic isotope effect (KIE) along with various electrochemical characterizations, we determined that the rate determining step (RDS) of the ORR is a proton-independent step when the density of Pt NPs on the surface of the carbon support is high. Upon decrease of the density of Pt NPs on the surface, the RDS of the ORR starts involving a proton, as denoted by an increase of the KIE >1. This underlined the critical role played by the carbon support in the oxygen reduction reaction electrocatalysis by Pt supported on high surface area carbon.

Nuclear Quantum Effects on Aqueous Electron Attachment and Redox Properties

Nuclear quantum effects (NQEs) on the reduction and oxidation properties of small aqueous species (CO₂, HO₂, and O₂) are quantified and rationalized by first-principles molecular dynamics and thermodynamic integration. Vertical electron attachment, or electron affinity, and detachment energies (VEA and VDE) are strongly affected by NQEs, decreasing in absolute value by 0.3 eV going from a classical to a quantum description of the nuclei. The effect is attributed to NQEs that lessen the solvent response upon oxidation/reduction. The reduction of solvent reorganization energy is expected to be general for small solutes in water. In the thermodynamic integral that yields the free energy of oxidation/reduction, these large changes enter with opposite sign, and only a small net effect (0.1 eV) remains. This is not obvious for CO₂, where the integrand is strongly influenced by NQEs due to the onset of interaction of the reduced orbital with the conduction band of the liquid during thermodynamic integration. We conclude that NQEs might not have to be included in the computation of redox potentials, unless high accuracy is needed, but are important for VEA and VDE calculations.