Minimum Energy Reaction Path Research Articles

Physical Prior Mean Function-Driven Gaussian Processes Search for Minimum-Energy Reaction Paths with a Climbing-Image Nudged Elastic Band: A General Method for Gas-Phase, Interfacial, and Bulk-Phase Reactions.

The climbing-image nudged elastic band (CI-NEB) method serves as an indispensable tool for computational chemists, offering insight into minimum-energy reaction paths (MEPs) by delineating both transition states (TSs) and intermediate nonstationary structures along reaction coordinates. However, executing CI-NEB calculations for reactions with extensive reaction coordinate spans necessitates a large number of images to ensure a reliable convergence of the MEPs and TS structures, presenting a computationally demanding optimization challenge, even with mildly costly electronic-structure methods. In this study, we advocate for the utilization of physically inspired prior mean function-based Gaussian processes (GPs) to expedite MEP exploration and TS optimization via the CI-NEB method. By incorporating reliable prior physical approximations into potential energy surface (PES) modeling, we demonstrate enhanced efficiency in multidimensional CI-NEB optimization with surrogate-based optimizers. Our physically informed GP approach not only outperforms traditional nonsurrogate-based optimizers in optimization efficiency but also on-the-fly learns the reaction path valley during optimization, culminating in significant advancements. The surrogate PES derived from our optimization exhibits high accuracy compared to true PES references, aligning with our emphasis on leveraging reliable physical priors for robust and efficient posterior mean learning in GPs. Through a systematic benchmark study encompassing various reaction pathways, including gas-phase, bulk-phase, and interfacial/surface reactions, our physical GPs consistently demonstrate superior efficiency and reliability. For instance, they outperform the popular fast inertial relaxation engine optimizer by approximately a factor of 10, showcasing their versatility and efficacy in exploring reaction mechanisms and surface reaction PESs.

The complex-formation dynamics of O + H(D)2+ (v = 0,1; j = 0) reactions on 12A'' and 12A′

The reactions O + H(D)2+ are studied based on the ground state potential energy surface (PES) 12A″ and the first excited PES 12A′. Both two potential energy surfaces comprise deep wells during the minimum energy reaction path. The average lifetimes of the complex-formation of the title reactions as a function of translational energy are calculated. The results indicated that the average lifetime of the complex-formation decreases with the increasing of collision energy for the two potential energy surfaces. There are two kinds of reaction mechanisms, one is direct reaction mechanism; another is indirect one. The indirect mechanism is dominated for all the collision energies studied. However, with the increasing of the collision energy, the direct reaction mechanism becomes more and more pronounced. Besides, the influences of reagent vibrational excitation and isotopic effect on the scalar properties and vector properties are studied in detail respectively in this work. The reagent vibrational excitation enhances the number of the direct reactive trajectories remarkably on 12A″, though it has nearly no influence on the average lifetime of the complex formation. In strong contrast, the reagent vibrational excitation suppresses the number of indirect reactive trajectories and reduces the average lifetime of the complex formation on the 12A′. The isotopic substitution has no influence on the scalar properties; however, it affects the vector properties strongly.

Ring-Polymer Instanton Tunneling Splittings of Tropolone and Isotopomers using a Δ-Machine Learned CCSD(T) Potential: Theory and Experiment Shake Hands.

Tropolone, a 15-atom cyclic molecule, has received much interest both experimentally and theoretically due to its H-transfer tunneling dynamics. An accurate theoretical description is challenging owing to the need to develop a high-level potential energy surface (PES) and then to simulate quantum-mechanical tunneling on this PES in full dimensionality. Here, we tackle both aspects of this challenge and make detailed comparisons with experiments for numerous isotopomers. The PES, of near CCSD(T)-quality, is obtained using a Δ-machine learning approach starting from a pre-existing low-level DFT PES and corrected by a small number of approximate CCSD(T) energies obtained using the fragmentation-based molecular tailoring approach. The resulting PES is benchmarked against DF-FNO-CCSD(T) and CCSD(T)-F12 calculations. Ring-polymer instanton calculations of the splittings, obtained with the Δ-corrected PES are in good agreement with previously reported experiments and a significant improvement over those obtained using the low-level DFT PES. The instanton path includes heavy-atom tunneling effects and cuts the corner, thereby avoiding passing through the conventional saddle-point transition state. This is in contradistinction with typical approaches based on the minimum-energy reaction path. Finally, the subtle changes in the splittings for some of the heavy-atom isotopomers seen experimentally are reproduced and explained.

Quantum mechanics/molecular mechanics studies on the mechanistic photophysics of sunscreen oxybenzone in methanol solution.

Herein, we have employed the QM(CASPT2//CASSCF)/MM method to explore the photophysical and photochemical mechanism of oxybenzone (OB) in methanol solution. Based on the optimized minima, conical intersections and crossing points, and minimum-energy reaction paths related to excited-state intramolecular proton transfer (ESIPT) and excited-state decay paths in the 1ππ*, 1nπ*, 3ππ*, 3nπ*, and S0 states, we have identified several feasible excited-state relaxation pathways for the initially populated S2(1ππ*) state to decay to the initial enol isomer' S0 state. The major one is the singlet-mediated and stretch-torsion coupled ESIPT pathway, in which the system first undergoes an essentially barrierless 1ππ* ESIPT process to generate the 1ππ* keto species, and finally realizes its ground state recovery through the subsequent carbonyl stretch-torsion facilitating S1 → S0 internal conversion (IC) and the reverse ground-state intramolecular proton transfer (GSIPT) process. The minor ones are related to intersystem crossing (ISC) processes. At the S2(1ππ*) minimum, an S2(1ππ*)/S1(1nπ*)/T2(3nπ*) three-state intersection region helps the S2 system branch into the T1 state through a S2 → S1 → T1 or S2 → T2 → T1 process. Once it has reached the T1 state, the system may relax to the S0 state via direct ISC or via subsequent nearly barrierless 3ππ* ESIPT to yield the T1 keto tautomer and ISC. The resultant S0 keto species significantly undergoes reverse GSIPT and only a small fraction yields the trans-keto form that relaxes back more slowly. However, due to small spin-orbit couplings at T1/S0 crossing points, the ISC to S0 state occurs very slowly. The present work rationalizes not only the ultrafast excited-state decay dynamics of OB but also its phosphorescence emission at low temperature.

Ab Initio Nonadiabatic Surface-Hopping Trajectory Simulations of Photocatalytic Water Oxidation and Hydrogen Evolution with the Heptazine Chromophore.

In the past decade, polymeric carbon nitrides consisting of heptazine (Hz) building blocks emerged as highly promising materials for photocatalytic hydrogen evolution from water or sacrificial electron donors with near-ultraviolet light. However, the complexity of these materials and their poor characterization at the atomic level are detrimental to the unraveling of the detailed mechanisms of the reactions leading to hydrogen evolution. Recently, it has been shown that a derivative of the Hz molecule, trianisole-heptazine (TAHz), is a potent photobase, which readily oxidizes various derivatives of phenol and even water by an excited-state proton-coupled electron-transfer (PCET) reaction. Energy profiles along minimum-energy reaction paths and relaxed PCET potential-energy surfaces, which previously were computed with ab initio electronic-structure methods for complexes of Hz and TAHz with protic substrates, led to qualitative insights. To obtain more quantitative insight, reaction dynamics simulations are required. In the present work, the time scales of the electron and proton transfer processes and the branching ratios of competing channels were explored with ab initio on-the-fly quasiclassical surface-hopping trajectory simulations for the hydrogen-bonded Hz-H2O complex. By the analysis of representative trajectories, detailed insight into the interplay of various nonadiabatic electronic transitions, electron transfer, proton transfer, and vibrational energy relaxation is obtained. The HzH radicals which are formed by the photoreduction of Hz can disproportionate to Hz and HzH2 in an exothermic reaction with a low reaction barrier. The time scales and branching ratios of competing channels in H-atom photodetachment from the HzH2 molecule also were explored with ab initio surface-hopping simulations. These results delineate for the first time a quantitatively supported scenario of water oxidation and hydrogen evolution with a molecular carbon nitride photocatalyst.

Insights into the Coadsorption and Reactivity of O and CO on Ru(0001) and Their Coverage Dependence

Using density functional theory and an exchange-correlationfunctional that includes the van der Waals interaction, we study the coadsorption of CO on Ru(0001) saturated with 0.5 ML of oxygen. Different coexisting CO coverages are considered that are experimentally motivated, the room temperaturecoverage consisting of 0.5 ML-O + 0.25 ML-CO (low coverage), the saturation coverage achieved at low temperatures (0.5 ML-O + 0.375 ML-CO, intermediate coverage), and the equally mixed monolayer that is stable according to our calculations but not experimentally observed yet (0.5 ML-O + 0.5 ML-CO, high coverage). For each coverage, we study the competition between the desorption and oxidation of CO on the corresponding optimized structure by analyzing their reaction energies and minimum energy reaction paths. The desorption process is endothermic at all coverages, although the desorption energy decreases as the CO coverage increases. The process itself (and also the reverted adsorption) becomes more involved at the intermediate and high coverages because of the appearance of a physisorption well and concomitant energy barrier separating it from the chemisorbed state. Remarkably, the oxidation of CO, which is endothermic at low coverages, turns exothermic at the intermediate and high coverages. In all cases, the minimum reaction path for oxidation, which involves the chemisorbed and physisorbed CO2, is ruled by one of the large energy barriers that protect these molecular states. Altogether, the larger activation energies for oxidation as compared to those for desorption and the extreme complexity of the oxidation against the desorption paths explain that CO desorption dominates over the oxidation in experiments.

Theoretical Modeling of Addition Reactions of an H2 Molecule to Mg17L Magnesium Clusters Doped with 3d Metals

The potential energy surface (PES) of the elementary catalytic cycle of hydrogenation of magnesium clusters doped with transition metals (L = Ti, V, Cr, Mn, Fe, Co), Mg17L + H2, has been calculated by the density functional theory method. Stationary points of the PES corresponding to local minima of intermediates and transition states along the minimum energy reaction path have been determined. The energies, geometries, and spectroscopic parameters of the stationary points have been calculated. Trends in the catalytic activity of dopants in the series of 3d metals have been studied. The results are compared with the data of previous DFT calculations of the catalytic cycle of hydrogenation Al12L + H2 for similar reactions of aluminum clusters with the same dopants L.

Computational Investigation of the Selective Cleavage of Diastereotopic Cyclopropane Bonds in 5-Spirocyclopropane Isoxazolidines Rearrangement.

The complete path of the Brandi-Guarna rearrangement of 5-spirocyclopropane isoxazolidines has been investigated by means of density functional theory calculations to rationalize the competing formation of tetrahydropyridones and enaminones by the determination of the minimum energy reaction paths. Our calculations confirm that the rearrangement is triggered by the homolysis of the isoxazolidine N-O bond followed by cleavage of one of the two C-CH2 cyclopropane bonds as previously proposed by the Fabian group [ Eur. J. Org. Chem. 2001, 2001, 4223]. In addition, the results of this work suggest that in the presence of a stereogenic center at isoxazolidine C-4', the formation of a piperidinone or an enaminone as the final product depends on which of the two diastereotopic C-CH2 bonds of cyclopropane is cleaved in the second step of the process. The result can be of great interest for the understanding of other processes involving the opening of a cyclopropane ring.

Geodesic interpolation for reaction pathways.

The development of high throughput reaction discovery methods such as the ab initio nanoreactor demands massive numbers of reaction rate calculations through the optimization of minimum energy reaction paths. These are often generated from interpolations between the reactant and product endpoint geometries. Unfortunately, straightforward interpolation in Cartesian coordinates often leads to poor approximations that lead to slow convergence. In this work, we reformulate the problem of interpolation between endpoint geometries as a search for the geodesic curve on a Riemannian manifold. We show that the perceived performance difference of interpolation methods in different coordinates is the result of an implicit metric change. Accounting for the metric explicitly allows us to obtain good results in Cartesian coordinates, bypassing the difficulties caused by redundant coordinates. Using only geometric information, we are able to generate paths from reactants to products which are remarkably close to the true minimum energy path. We show that these geodesic paths are excellent starting guesses for minimum energy path algorithms.

Theoretical analysis of the time-resolved binary (e, 2e) binding energy spectra on three-body photodissociation of acetone at 195 nm

We report on theoretical progress in time-resolved (e, 2e) electron momentum spectroscopy of photodissociation dynamics of the deuterated acetone molecule at 195 nm. We have examined the predicted minimum energy reaction path to investigate whether associated (e, 2e) calculations meet the experimental results. A noticeable difference between the experiment and calculations has been found at around binding energy of 10 eV, suggesting that the observed difference may originate, at least partly, in ever-unconsidered non-minimum energy paths.

A global potential energy surface and time‐dependent quantum wave packet calculation of Au + H2 reaction

AbstractA global potential energy surface (PES) corresponding to the ground state of AuH2 system has been constructed based on 22 853 ab initio energies calculated by the multireference configuration interaction method with a Davidson correction. The neural network method is used to fit the PES, and the root mean square error is only 1.87 meV. The topographical features of the novel global PES are compared with previous PES which is constructed by Zanchet et al. (Zanchet PES). The global minimum energy reaction paths on the two PESs both have a well and a barrier. Relative to the Au + H2 reactants, the energy of well is 0.316 eV on the new PES, which is 0.421 eV deeper than Zanchet PES. The calculation of Au(2S) + H2(X1Σg+) → AuH(X1Σ+) + H(2S) dynamical reaction is carried out on new PES, by the time‐dependent quantum wave packet method (TDWP) with second order split operator. The reaction probabilities, integral cross‐sections (ICSs) and differential cross‐sections are obtained from the dynamics calculation. The threshold in the reaction is about 1.46 eV, which is 0.07 eV smaller than Zanchet PES due to the different endothermic energies on the two PESs. At low collision energy (<2.3 eV), the total ICS is larger than the result obtained on Zanchet PES, which can be attributed to the difference of the wells and endothermic energies.

Experimental and theoretical progress in time-resolved (e, 2e) electron momentum spectroscopy of photodissociation dynamics of acetone at 195 nm

SynopsisWe report on experimental and theoretical progress in time-resolved (e, 2e) electron momentum spectroscopy of photodissociation dynamics of the deuterated acetone molecule at 195 nm. Experimentally, we are conducting a series of measurements to have improved experimental results, compared to the earlier ones, by using a pump laser with higher intensity. Theoretically, we have examined the predicted minimum energy reaction path to investigate whether associated (e, 2e) calculations meet the experimental results. A noticeable difference between the experiment and the calculations has been found at around binding energy of 10 eV, suggesting that the observed difference may originate, at least partly, in ever-unconsidered non-minimum energy paths.

Does the S-H Bond Always Break after Adsorption of an Alkylthiol on Au(111)?

The reaction mechanism for the formation of alkyl thiol self-assembled monolayers (SAM) on Au(111) is still not clearly understood. Especially, the role of defects on the chemisorption process is an important goal to be addressed. In this work, different minimum energy reaction paths for R-SH dissociation of thiols (with long and short chains and dithiol species) adsorbed on gold adatom are calculated by using periodic density functional theory (DFT). Our results show a lower energy barrier for the RS-H bond dissociation when two thiols are adsorbed per adatom. In addition, in contrast with the formation of an adatom at the Au(111) which has been shown to depend on the alkyl chain length, the activation energy of the RS-H bond dissociation of thiols adsorbed on an adatom was shown to be independent of the alkyl chain length. The presented results and derived hypothesis support the model that thiols with long alkyl chain thiols mainly adsorb molecularly on Au(111), while for short alkyl chain thiols the S-H bond breaks. This result is explained by the fact that short-chain thiols have lower interchain interaction energies and are thus more mobile compared to the long alkyl chain thiols on the Au(111) surface. This feature enables the short chains to reach adequate geometries, driven by entropy, which could deform the Au(111) more drastically and probably pull Au atoms out from surface to form adatoms. With these results a new mechanism is proposed for the formation of alkyl chain thiols on Au(111).

Different QM/MM Approaches To Elucidate Enzymatic Reactions: Case Study on ppGalNAcT2.

Hybrid QM/MM computational studies can provide invaluable insight into the mechanisms of enzymatic reactions that can be exploited for rational drug design. Various approaches are available for such studies. However, their strengths and weaknesses may not be immediately apparent. Using the retaining glycosyltransferase ppGalNAcT2 as a case study, we compare different methodologies used to obtain reaction paths and transition state information. Ab Initio MD using CPMD coupled with the String Method is used to derive the minimum free energy reaction path. The geometrical features of the free energy path, especially around the transition state, agree with the minimum potential energy path obtained by the much less computationally expensive Nudged Elastic Band method. The barrier energy, however, differs by 8 kcal/mol. The free energy surface generated by metadynamics provides a rough overview of the reaction and can confirm the physical relevance of optimized paths or provide an initial guess for path optimization methods. Calculations of enzymatic reactions are usually performed at best at the DFT level of theory. A comparison of widely used functionals with high-level DLPNO-CCSD(T)/CBS data on the potential energy profile serves as a validation of the usability of DFT for this type of enzymatic reaction. The M06-2X meta-hybrid functional in particular matches the DLPNO-CCSD(T)/CBS reference extremely well with errors within 1 kcal/mol. However, even pure-GGA functional OPBE provides sufficient accuracy for this type of study.

Photodynamics of oxybenzone sunscreen: Nonadiabatic dynamics simulations.

Herein we have used combined static electronic structure calculations and "on-the-fly" global-switching trajectory surface-hopping dynamics simulations to explore the photochemical mechanism of oxybenzone sunscreen. We have first employed the multi-configurational CASSCF method to optimize minima, conical intersections, and minimum-energy reaction paths related to excited-state intramolecular proton transfer (ESIPT) and excited-state decays in the (1)ππ(∗), (1)nπ(∗), and S0 states (energies are refined at the higher MS-CASPT2 level). According to the mapped potential energy profiles, we have identified two ultrafast excited-state deactivation pathways for the initially populated (1)ππ(∗) system. The first is the diabatic ESIPT process along the (1)ππ(∗) potential energy profile. The generated (1)ππ(∗) keto species then decays to the S0 state via the keto (1)ππ(∗)/gs conical intersection. The second is internal conversion to the dark (1)nπ(∗) state near the (1)ππ(∗) /(1)nπ(∗) crossing point in the course of the diabatic (1)ππ(∗) ESIPT process. Our following dynamics simulations have shown that the ESIPT and (1)ππ(∗) → S0 internal conversion times are 104 and 286 fs, respectively. Finally, our present work demonstrates that in addition to the ESIPT process and the (1)ππ(∗) → S0 internal conversion in the keto region, the (1)ππ(∗) → (1)nπ(∗) internal conversion in the enol region plays as well an important role for the excited-state relaxation dynamics of oxybenzone.

Excited-State Proton Transfer and Decay in Hydrogen-Bonded Oxazole System: MS-CASPT2//CASSCF Study

Herein we have employed high-level multi-reference CASSCF and MS-CASPT2 electronic structure methods to systematically study the photochemical mechanism of intramolecularly hydrogen-bonded 2-(2′-hydroxyphenyl)-4-methyloxazole. At the CASSCF level, we have optimized minima, conical intersections, minimum-energy reaction paths relevant to the excited-state intramolecular proton transfer (ESIPT), rotation, photoisomerization, and the excited-state deactivation pathways. The energies of all structures and paths are refined by the MS-CASPT2 method. On the basis of the present results, we found that the ESIPT process in a conformer with the OH···N hydrogen bond is essentially barrierless process; whereas, the ESIPT process is inhibited in the other conformer with the OH···O hydrogen bond. The central single-bond rotation of the S1 enol species is energetically unfavorable due to a large barrier. In addition, the excited-state deactivation of the S1 keto species, as a result of the ultrafast ESIPT, is very efficient because of the existence of two easily-approached keto S1/S0 conical intersections. In stark contrast to the S1 keto species, the decay of the S1 enol species is almostly blocked. The present theoretical study contributes valuable knowledge to the understanding of photochemistry of similar intramolecularly hydrogen-bonded molecular and biological systems.

Molecular pathways of SOCl2 hydrolysis within mono- and diaqua complexes. A quantum chemical study

Quantum chemistry methods (DFT, MP2, G4, and CCSD(T)) were used to calculate the energies, thermodynamic and kinetic parameters of elementary reactions of thionyl chloride (SOCl2) hydrolysis in the gas phase involving bi- and termolecular complexes. Optimization of molecular geometry and search for all the intermediates and transition states were performed at the B3LYP/6-311++G(2d,2p) and MP2/6-311++G(3df,3pd) levels. For the key stationary points, the CCSD(T)/cc-pVDZ and CCSD(T)/aug-cc-pVTZ optimizations were carried out. For both bi- and termolecular reactions, overall minimum energy reaction paths were constructed to connect all the discovered stationary points. The results show that water dimers involvement leads to a significant decrease in activation energy but not in the Gibbs free energy of activation. It was discovered that the termolecular hydrolysis of first SCl bond consists of two steps and runs through the intermediate in which the coordinated SOCl2 molecule has a flat structure.

Stepwise catalytic mechanism via short-lived intermediate inferred from combined QM/MM MERP and PES calculations on retaining glycosyltransferase ppGalNAcT2.

The glycosylation of cell surface proteins plays a crucial role in a multitude of biological processes, such as cell adhesion and recognition. To understand the process of protein glycosylation, the reaction mechanisms of the participating enzymes need to be known. However, the reaction mechanism of retaining glycosyltransferases has not yet been sufficiently explained. Here we investigated the catalytic mechanism of human isoform 2 of the retaining glycosyltransferase polypeptide UDP-GalNAc transferase by coupling two different QM/MM-based approaches, namely a potential energy surface scan in two distance difference dimensions and a minimum energy reaction path optimisation using the Nudged Elastic Band method. Potential energy scan studies often suffer from inadequate sampling of reactive processes due to a predefined scan coordinate system. At the same time, path optimisation methods enable the sampling of a virtually unlimited number of dimensions, but their results cannot be unambiguously interpreted without knowledge of the potential energy surface. By combining these methods, we have been able to eliminate the most significant sources of potential errors inherent to each of these approaches. The structural model is based on the crystal structure of human isoform 2. In the QM/MM method, the QM region consists of 275 atoms, the remaining 5776 atoms were in the MM region. We found that ppGalNAcT2 catalyzes a same-face nucleophilic substitution with internal return (SNi). The optimized transition state for the reaction is 13.8 kcal/mol higher in energy than the reactant while the energy of the product complex is 6.7 kcal/mol lower. During the process of nucleophilic attack, a proton is synchronously transferred to the leaving phosphate. The presence of a short-lived metastable oxocarbenium intermediate is likely, as indicated by the reaction energy profiles obtained using high-level density functionals.

Photoinduced oxidation of water in the pyridine-water complex: comparison of the singlet and triplet photochemistries.

It has recently been shown that low-lying dark charge-separated singlet excited states of nπ* and ππ* character exist in the hydrogen-bonded pyridine-water complex in addition to the familiar nπ* and ππ* excited states of the pyridine chromophore. The former have been shown to promote the transfer of a proton from water to pyridine, resulting in the pyridinyl-hydroxyl radical pair. In the present work, the potential-energy surfaces of the triplet excited states of the pyridine-water complex have been explored with the same ab initio electronic-structure methods (ADC(2), CASPT2). Minimum-energy reaction paths for excited-state H atom transfer, energy surfaces in the vicinity of the barrier for H atom transfer, as well as multistate surface crossings have been characterized. The photochemical reaction mechanisms on the singlet and triplet potential-energy surfaces are compared, and their relevance for photoinduced water oxidation with the pyridine chromophore are discussed.

Reaction of CH3CHO with Y+: A density functional theoretical study

The reaction mechanism of the Y+ cation with CH3CHO has been investigated with a DFT approach. All the stationary points are determined at the UB3LYP/ECP/6-311++G** level of the theory. Both ground and excited state potential energy surfaces are investigated in detail. The present results show that the title reaction start with the formation of a CH3CHO-metal complex followed by C-C, aldehyde C-H, methyl C-H and C-O activation. These reactions can lead to four different products (Y+CH4 + CO, Y+CO + CH4, Y+COCH2 + H2 and Y+O + C2H4). The minimum energy reaction path is found to involve the spin inversion in the different reaction steps, this potential energy curve-crossing dramatically affects reaction exothermic. The present results may be helpful in understanding the mechanism of the title reaction and further experimental investigation of the reaction.