Kinetic isotope effects and how to describe them

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

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.

Quantum Molecular Devices

Miniaturization has been the driving force in contemporary technologies. However, two main obstacles limit further progress: additional reduction in size has reached its quantum limit, and lithography has reached its threshold. Future progress requires tackling three challenges: chemical synthesis of a complete device, active cooling for exploiting quantum characteristics, and quantum coherent control for operation. Chemical synthesis replaces the current top-bottom approach to manufacturing with bottom-up synthesis from elementary building blocks. New ultracold synthetic methods should be developed. An additional challenge is the active cooling of molecules, where the bottleneck is entropy removal. Notably, the current solution, namely, diffusion, is too slow. A coherent approach offers a possible solution; specifically, quantum coherent control is the method of choice for manipulating ultracold matter. Finally, the many degrees of freedom of molecules should be an asset that allows the design and implementation of complex tasks such as sensing communication and computing.

Measurement of kinetic isotope effects on peptide hydroxylation using MALDI-MS

Primary kinetic isotope effects (KIEs) provide unique insight into enzymatic reactions, as they can reveal rate-limiting steps and detailed chemical mechanisms. HIF hydroxylases, part of a family of 2-oxoglutarate (2OG) oxygenases are central to the regulation of many crucial biological processes through O2-sensing, but present a challenge to monitor due to the large size of the protein substrate and the similarity between native and hydroxylated substrate. MALDI-TOF MS is a convenient tool to measure peptide masses, which can also be used to measure the discontinuous kinetics of peptide hydroxylation for Factor Inhibiting HIF (FIH). Using this technique, rate data can be observed from the mole-fraction of CTAD and CTAD-OH in small volumes, allowing noncompetitive H/D KIEs to be measured. Slow dCTAD substrate leads to extensive uncoupling of O2 consumption from peptide hydroxylation, leading to enzyme autohydroxylation, which is observed using UV-vis spectroscopy. Simultaneously measuring both the normal product, CTAD-OH, and the uncoupled product, autohydroxylated enzyme, the KIE on the microscopic step of hydrogen atom transfer (HAT) can be estimated. MALDI-MS analysis is a strong method for monitoring reactions that hydroxylate peptides, and can be generalized to other similar reactions, and simultaneous kinetic detection of branched products can provide valuable insight on microscopic KIEs at intermediate mechanistic steps.

Hydrogen Tunneling in Catalytic Hydrolysis and Alcoholysis of Silanes

An unprecedented quantum tunneling effect has been observed in catalytic Si−H bond activations at room temperature. The cationic hydrido‐silyl‐iridium(III) complex, {Ir[SiMe(o‐C₆H₄SMe)₂](H)(PPh₃)(THF)}[BAr^F₄], has proven to be a highly efficient catalyst for the hydrolysis and the alcoholysis of organosilanes. When triethylsilane was used as a substrate, the system revealed the largest kinetic isotopic effect (KIE_{Si−H/Si−D}=346±4) ever reported for this type of reaction. This unexpectedly high KIE, measured at room temperature, together with the calculated Arrhenius preexponential factor ratio (A_H/A_D=0.0004) and difference in the observed activation energy [(EaD −EaH )=34.07 kJ mol⁻¹] are consistent with the participation of quantum tunneling in the catalytic process. DFT calculations have been used to unravel the reaction pathway and identify the rate‐determining step. Aditionally, isotopic effects were considered by different methods, and tunneling effects have been calculated to be crucial in the process.

Instanton theory for Fermi's golden rule and beyond

Instanton theory provides a semiclassical approximation for computing quantum tunnelling effects in complex molecular systems. It is typically applied to proton-transfer reactions for which the Born-Oppenheimer approximation is valid. However, many processes in physics, chemistry and biology, such as electron transfers, are non-adiabatic and are correctly described instead using Fermi's golden rule. In this work, we discuss how instanton theory can be generalized to treat these reactions in the golden-rule limit. We then extend the theory to treat fourth-order processes such as bridge-mediated electron transfer and apply the method to simulate an electron moving through a model system of three coupled quantum dots. By comparison with benchmark quantum calculations, we demonstrate that the instanton results are much more reliable than alternative approximations based on superexchange-mediated effective coupling or a classical sequential mechanism. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Electro-Oxidative C-N Bond Formation through Azolation of Indole Derivatives: An Access to 3-Substituent-2-(Azol-1-yl)indoles

A practical protocol to synthesize 3-substituent-2-(azol-1-yl)indole derivatives has been developed via an electrochemical oxidative cross coupling process under mild conditions. This electro-oxidative C-N bond formation strategy tolerates a range of functional groups and is amenable to gram scale synthesis. Moreover, this method was applied to the late-stage functionalization of bioactive molecules.

Reply to the 'Comment on "Topography of the Free Energy Landscape on the Claisen-Schmidt Condensation: Solvent and Temperature Effect in the Rate-Controlling Step"' by N. D. Coutinho, H. G. Machado, V. H. Carvalho-Silva and W. A. da Silva, Phys. Chem. Chem. Phys., 2021, , 6738

In the Comment on our paper on the description of the Gibbs Free energy profile of Claisen-Schmidt condensation, it is claimed that our calculations are flawed due to inconsistencies with experimental isotope effects in aqueous acetonitrile. In this Reply, we presented rigorous arguments, ambiguities in the Comment and new calculations confirming the consistency of our results: (i) small differences in the relative energetic barriers in both experimental and theoretical curves make the assignment of the rate-limiting step debatable, making the concept of RCS questionable; (ii) it is shown how the misinterpretation of the elementary steps and of the overall processes rate constants led the Comment to incorrect conclusions about the behavior of the inverse isotopic effect; (iii) neglect in the Comment of the inverse kinetic isotope effect in step R2 due to the hybridization conversion, and of the inverse equilibrium isotopic effect for step R1 to describe an overall iKIE > 1, (iv) an erroneous suggestion in the Comment that the disagreement between experimental kinetic parameters is due to the fact that acetonitrile is not used in previous experimental works, when contradictorily the literature recommends it as being indispensable to allow kinetic accuracy; and (v) new calculations improved by explicit-implicit hybrid treatment again ensure that step R4, and not step R5, can assume the role of RCS in protic solvents. Recognizing that questioning is an excellent path for promoting understanding, we hope that the answers provided here will help to clarify and expand the pertinent topics under discussion.

Impact of the Characteristics of Quantum Chemical Databases on Machine Learning Prediction of Tautomerization Energies

An essential aspect for adequate predictions of chemical properties by machine learning models is the database used for training them. However, studies that analyze how the content and structure of the databases used for training impact the prediction quality are scarce. In this work, we analyze and quantify the relationships learned by a machine learning model (Neural Network) trained on five different reference databases (QM9, PC9, ANI-1E, ANI-1, and ANI-1x) to predict tautomerization energies from molecules in Tautobase. For this, characteristics such as the number of heavy atoms in a molecule, number of atoms of a given element, bond composition, or initial geometry on the quality of the predictions are considered. The results indicate that training on a chemically diverse database is crucial for obtaining good results and also that conformational sampling can partly compensate for limited coverage of chemical diversity. The overall best-performing reference database (ANI-1x) performs on average by 1 kcal/mol better than PC9, which, however, contains about 2 orders of magnitude fewer reference structures. On the other hand, PC9 is chemically more diverse by a factor of ∼5 as quantified by the number of atom-in-molecule-based fragments (amons) it contains compared with the ANI family of databases. A quantitative measure for deficiencies is the Kullback-Leibler divergence between reference and target distributions. It is explicitly demonstrated that when certain types of bonds need to be covered in the target database (Tautobase) but are undersampled in the reference databases, the resulting predictions are poor. Examples of this include the poor performance of all databases analyzed to predict C(sp²)-C(sp²) double bonds close to heteroatoms and azoles containing N-N and N-O bonds. Analysis of the results with a Tree MAP algorithm provides deeper understanding of specific deficiencies in predicting tautomerization energies by the reference datasets due to inadequate coverage of chemical space. Capitalizing on this information can be used to either improve existing databases or generate new databases of sufficient diversity for a range of machine learning (ML) applications in chemistry.

Understanding the Large Kinetic Isotope Effect of Hydrogen Tunneling in Condensed Phases by Using Double-Well Model Systems

In recent years, many experiments have shown large kinetic isotope effects (KIEs) for hydrogen transfer reactions in condensed phases as evidence of strong quantum tunneling effects. Since accurate calculation of the tunneling dynamics in such systems still present significant challenges, previous studies have employed different types of approximations to estimate the tunneling effects and KIEs. In this work, by employing model systems consisting of a double-well coupled to a harmonic bath, we calculate the tunneling effects and KIEs using the numerically exact hierarchical equations of motion (HEOM) method. It is found that hydrogen and deuterium transfer reactions in the same system may show rather different behaviors, where hydrogen transfer is dominated by tunneling between the two lowest vibrational states and deuterium transfer is controlled by excited vibrational states close to the barrier top. The simulation results are also used to test the validity of various approximate methods. It is shown that the Wolynes theory of dissipative tunneling gives a good estimation of rate constants in the over-the-barrier regime, while the nonadiabatic reaction rate theory based on the Landau-Zener formula is more suitable for deep tunneling reactions.

Perturbing the O-H…O Hydrogen Bond in 1-oxo-3-hydroxy-2-propene

Ab initio MP2/aug'-cc-pVTZ calculations have been carried out to identify and characterize equilibrium structures and transition structures on the 1-oxo-3-hydroxy-2-propene: Lewis acid potential energy surfaces, with the acids LiH, LiF, BeH2, and BeF2. Two equilibrium structures, one with the acid interacting with the C=O group and the other with the interaction occurring at the O-H group, exist on all surfaces. These structures are separated by transition structures that present the barriers to the interconversion of the two equilibrium structures. The structures with the acid interacting at the C=O group have the greater binding energies. Since the barriers to convert the structures with interaction occurring at the O-H group are small, only the isomers with interaction occurring at the C=O group could be experimentally observed, even at low temperatures. Charge-transfer energies were computed for equilibrium structures, and EOM-CCSD spin-spin coupling constants 2hJ(O-O), 1hJ(H-O), and 1J(O-H) were computed for equilibrium and transition structures. These coupling constants exhibit a second-order dependence on the corresponding distances, with very high correlation coefficients.

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.

Evaluation of Poorly Soluble Drugs' Dissolution Rate by Laser Scattering in Different Water Isotopologues

The most important task in the design of dosage forms is to modify the pharmaceutical substances structure in order to increase solubilization, targeted delivery, controlled rate of drug administration, and its bioavailability. Screening-laboratory (in vitro) or computer (in silico)-as a procedure for selecting a prototype for the design of a drug molecule, involves several years of research and significant costs. Among a large number of solvents and diluents (alcohol, ether, oils, glycerol, Vaseline) used in the pharmaceutical industry for the manufacture of drugs water finds the greatest application. This is because all biological reactions (reactions in living systems) take place in water and distribution of the fluid in the body and the substances found within is critical for the maintenance of intracellular and extracellular functions. Modern studies in the field of the stable isotopic compositions of natural water and its structure and properties make it possible to use isotopic transformations of the water to improve the pharmacokinetic properties of medicinal substances without previous structural modification. It is known that by replacing any of the atoms in the reacting substance molecule with its isotope, it is possible to record changes in the reactivity, which are expressed as a change in the reaction rate constant, i.e., in the manifestation of the kinetic isotope effect (KIE). The article presents the results of studies on the effect of the kinetic isotope effect of a solvent-water-on increasing the solubility and dissolution rate constants of poorly soluble drugs using laser diffraction spectroscopy. The results of the studies can be successfully implemented in pharmaceutical practice to overcome the poor solubility of medicinal substances of classes II and IV, according to the biopharmaceutical classification system (BCS), in water for pharmaceutical purposes by performing its preliminary and safe isotopic modification.

Microcanonical Tunneling Rates from Density-of-States Instanton Theory

Semiclassical instanton theory is a form of quantum transition-state theory which can be applied to the computation of thermal reaction rates in complex molecular systems including quantum tunneling effects. There have been a number of attempts to extend the theory to treat microcanonical rates. However, the previous formulations are either computationally unfeasible for large systems due to an explicit sum over states or they involve extra approximations, which make them less reliable. We propose a robust and practical microcanonical formulation called density-of-states instanton theory, which avoids the sum over states altogether. In line with the semiclassical approximations inherent to the instanton approach, we employ the stationary-phase approximation to the inverse Laplace transform to obtain the densities of states. This can be evaluated using only post-processing of the data available from a small set of instanton calculations, such that our approach remains computationally efficient. We show that the new formulation predicts results that agree well with quantum scattering theory for an atom-diatom reaction and with experiments for a photoexcited unimolecular hydrogen transfer in a Criegee intermediate. When the thermal rate is evaluated from a Boltzmann average over our new microcanonical formalism, it can overcome some problems of conventional instanton theory. In particular, it predicts a smooth transition at the crossover temperature and is able to describe bimolecular reactions with pre-reactive complexes such as CH₃OH + OH.

Instanton theory of tunneling in molecules with asymmetric isotopic substitutions

We consider quantum tunneling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. In a molecular context, this situation can arise if the symmetry is broken by isotopic substitutions. We derive a generalization of instanton theory for these asymmetric systems, leading to a semiclassical expression for the tunneling matrix element and hence the energy-level splitting. We benchmark the method using a set of one- and two-dimensional models, for which the results compare favorably with numerically exact quantum calculations. Using the ring-polymer instanton approach, we apply the method to compute the level splittings in various isotopomers of malonaldehyde in full dimensionality and analyze the relative contributions from the zero-point energy difference and tunneling effects.

Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane

Thermal rate constants for Mu + CH₄, Mu + C₂H₆ and Mu + C₃H₈ and their equivalent reactions with H were evaluated with ab initio instanton rate theory. The potential-energy surfaces are fitted using Gaussian process regression to high-level electronic-structure calculations evaluated around the tunnelling pathway. This method was able to successfully reproduce various experimental measurements for the rate constant of these reactions. However, it was not able to reproduce the faster-than-expected rate of Mu + C₃H₈ at 300 K reported by Fleming et al. [Phys. Chem. Chem. Phys., 2015, 17, 19901 and Phys. Chem. Chem. Phys., 2020, 22, 6326]. Analysis of our results indicates that the kinetic isotope effect at this temperature is not significantly influenced by quantum tunnelling. We consider many possible factors for the discrepancy between theory and experiment but conclude that in each case, the instanton approximation is unlikely to be the cause of the error. This is in part based on the good agreement we find between the instanton predictions and new multiconfigurational time-dependent Hartree (MCTDH) calculations for Mu + CH₄ using the same potential-energy surface. Further experiments will therefore be needed to resolve this issue.

Revisiting nuclear tunnelling in the aqueous ferrous–ferric electron transfer

We find that golden-rule quantum transition-state theory predicts nearly an order of magnitude less tunnelling than some of the previous estimates. This may indicate that the spin-boson model of electron transfer is not valid in the quantum regime.

Ab initio instanton rate theory made efficient using Gaussian process regression

Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into the calculations of chemical reaction rates based on a potential-energy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but it is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but it requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.